17 List of examples¶
List of examples shipped in the distribution of Optimizer API for C:
File |
Description |
|---|---|
A simple problem with one affine conic constraint (ACC) |
|
A simple problem with two affine conic constraints (ACC) |
|
Demonstrates the MOSEK interface to BLAS/LAPACK linear algebra routines |
|
An example of data/progress callback |
|
A simple conic exponential problem |
|
Implementation of a concurrent optimizer for linear and mixed-integer problems |
|
A simple conic quadratic problem |
|
A simple problem with disjunctive constraints (DJC) |
|
Demonstrates how error reporting can be customized |
|
A simple example of how to repair an infeasible problem |
|
A simple geometric program (GP) in conic form |
|
A Hello World example |
|
A simple linear problem |
|
A simple linear problem |
|
Implements logistic regression and simple log-sum-exp (CEO) |
|
A simple mixed-integer conic problem |
|
A simple mixed-integer linear problem |
|
A simple mixed-integer linear problem with an initial guess |
|
Uses MOSEK OptServer to solve an optimization problem asynchronously |
|
Uses MOSEK OptServer to solve an optimization problem synchronously |
|
Demonstrates parallel optimization using a batch method in MOSEK |
|
Shows how to set optimizer parameters and read information items |
|
Shows how to obtain and analyze a primal infeasibility certificate |
|
Portfolio optimization - basic Markowitz model |
|
Portfolio optimization - efficient frontier |
|
Portfolio optimization - market impact costs |
|
Portfolio optimization - transaction costs |
|
Portfolio optimization - cardinality constraints |
|
Portfolio optimization - factor model |
|
A simple power cone problem |
|
A simple quadratically constrained quadratic problem |
|
A simple quadratic problem |
|
Demonstrate how to modify and re-optimize a linear problem |
|
Demonstrates proper response handling |
|
A simple semidefinite problem with one matrix variable and a quadratic cone |
|
A simple semidefinite problem with two matrix variables |
|
A simple semidefinite problem with an LMI using the SVEC domain. |
|
Sensitivity analysis performed on a small linear problem |
|
A simple I/O example: read problem from a file, solve and write solutions |
|
Demonstrates how to examine the quality of a solution |
|
Demonstrates solving a linear system with the basis matrix |
|
Demonstrates solving a general linear system |
|
Shows how to find a Cholesky factorization of a sparse matrix |
|
Demonstrates string conversion to Unicode |
Additional examples can be found on the MOSEK website and in other MOSEK publications.
acc1.c
/*
Copyright: Copyright (c) MOSEK ApS, Denmark. All rights reserved.
File: acc1.c
Purpose : Tutorial example for affine conic constraints.
Models the problem:
maximize c^T x
subject to sum(x) = 1
gamma >= |Gx+h|_2
*/
#include <stdio.h>
#include "mosek.h" /* Include the MOSEK definition file. */
static void MSKAPI printstr(void *handle,
const char str[])
{
printf("%s", str);
} /* printstr */
int main(int argc, const char *argv[])
{
MSKrescodee r;
MSKint32t i, j;
MSKenv_t env = NULL;
MSKtask_t task = NULL;
MSKint64t quadDom;
/* Input data dimensions */
const MSKint32t n = 3,
k = 2;
/* Create the mosek environment. */
r = MSK_makeenv(&env, NULL);
if (r == MSK_RES_OK)
{
/* Create the optimization task. */
r = MSK_maketask(env, 0, 0, &task);
if (r == MSK_RES_OK)
{
MSK_linkfunctotaskstream(task, MSK_STREAM_LOG, NULL, printstr);
/* Create n free variables */
if (r == MSK_RES_OK)
r = MSK_appendvars(task, n);
if (r == MSK_RES_OK)
r = MSK_putvarboundsliceconst(task, 0, n, MSK_BK_FR, -MSK_INFINITY, +MSK_INFINITY);
/* Set up the objective */
{
double c[] = {2.0, 3.0, -1.0};
if (r == MSK_RES_OK)
r = MSK_putcslice(task, 0, n, c);
if (r == MSK_RES_OK)
r = MSK_putobjsense(task, MSK_OBJECTIVE_SENSE_MAXIMIZE);
}
/* One linear constraint sum(x) == 1 */
if (r == MSK_RES_OK)
r = MSK_appendcons(task, 1);
if (r == MSK_RES_OK)
r = MSK_putconbound(task, 0, MSK_BK_FX, 1.0, 1.0);
for(i = 0; i < n && r == MSK_RES_OK; i++)
r = MSK_putaij(task, 0, i, 1.0);
/* Append empty AFE rows for affine expression storage */
if (r == MSK_RES_OK)
r = MSK_appendafes(task, k + 1);
{
/* Fill in the affine expression storage with data */
/* F matrix in sparse form */
MSKint64t Fsubi[] = {1, 1, 2, 2}; /* G is placed from row 1 of F */
MSKint32t Fsubj[] = {0, 1, 0, 2};
double Fval[] = {1.5, 0.1, 0.3, 2.1};
int numEntries = 4;
/* Other data */
double h[] = {0, 0.1};
double gamma = 0.03;
/* Fill in F storage */
if (r == MSK_RES_OK)
r = MSK_putafefentrylist(task, numEntries, Fsubi, Fsubj, Fval);
/* Fill in g storage */
if (r == MSK_RES_OK)
r = MSK_putafeg(task, 0, gamma);
if (r == MSK_RES_OK)
r = MSK_putafegslice(task, 1, k+1, h);
}
/* Define a conic quadratic domain */
if (r == MSK_RES_OK)
r = MSK_appendquadraticconedomain(task, k + 1, &quadDom);
{
/* Create the ACC */
MSKint64t afeidx[] = {0, 1, 2};
if (r == MSK_RES_OK)
r = MSK_appendacc(task,
quadDom, /* Domain index */
k + 1, /* Dimension */
afeidx, /* Indices of AFE rows [0,...,k] */
NULL); /* Ignored */
}
/* Begin optimization and fetching the solution */
if (r == MSK_RES_OK)
{
MSKrescodee trmcode;
/* Run optimizer */
r = MSK_optimizetrm(task, &trmcode);
/* Print a summary containing information
about the solution for debugging purposes*/
MSK_solutionsummary(task, MSK_STREAM_MSG);
if (r == MSK_RES_OK)
{
MSKsolstae solsta;
MSK_getsolsta(task, MSK_SOL_ITR, &solsta);
switch (solsta)
{
case MSK_SOL_STA_OPTIMAL:
{
double *xx, *doty, *activity = NULL;
/* Fetch the solution */
xx = calloc(n, sizeof(double));
MSK_getxx(task,
MSK_SOL_ITR, /* Request the interior solution. */
xx);
printf("Optimal primal solution\n");
for (j = 0; j < n; ++j)
printf("x[%d]: %e\n", j, xx[j]);
free(xx);
/* Fetch the doty dual of the ACC */
doty = calloc(k + 1, sizeof(double));
MSK_getaccdoty(task,
MSK_SOL_ITR, /* Request the interior solution. */
0, /* ACC index. */
doty);
printf("Dual doty of the ACC\n");
for (j = 0; j < k + 1; ++j)
printf("doty[%d]: %e\n", j, doty[j]);
free(doty);
/* Fetch the activity of the ACC */
activity = calloc(k + 1, sizeof(double));
MSK_evaluateacc(task,
MSK_SOL_ITR, /* Request the interior solution. */
0, /* ACC index. */
activity);
printf("Activity of the ACC\n");
for (j = 0; j < k + 1; ++j)
printf("activity[%d]: %e\n", j, activity[j]);
free(activity);
}
break;
case MSK_SOL_STA_DUAL_INFEAS_CER:
case MSK_SOL_STA_PRIM_INFEAS_CER:
printf("Primal or dual infeasibility certificate found.\n");
break;
case MSK_SOL_STA_UNKNOWN:
printf("The status of the solution could not be determined. Termination code: %d.\n", trmcode);
break;
default:
printf("Other solution status.");
break;
}
}
else
{
printf("Error while optimizing.\n");
}
}
if (r != MSK_RES_OK)
{
/* In case of an error print error code and description. */
char symname[MSK_MAX_STR_LEN];
char desc[MSK_MAX_STR_LEN];
printf("An error occurred while optimizing.\n");
MSK_getcodedesc(r,
symname,
desc);
printf("Error %s - '%s'\n", symname, desc);
}
}
/* Delete the task and the associated data. */
MSK_deletetask(&task);
}
/* Delete the environment and the associated data. */
MSK_deleteenv(&env);
return (r);
} /* main */
acc2.c
/*
Copyright: Copyright (c) MOSEK ApS, Denmark. All rights reserved.
File: acc2.c
Purpose : Tutorial example for affine conic constraints.
Models the problem:
maximize c^T x
subject to sum(x) = 1
gamma >= |Gx+h|_2
This version inputs the linear constraint as an affine conic constraint.
*/
#include <stdio.h>
#include "mosek.h" /* Include the MOSEK definition file. */
static void MSKAPI printstr(void *handle,
const char str[])
{
printf("%s", str);
} /* printstr */
int main(int argc, const char *argv[])
{
MSKrescodee r;
MSKint32t i, j;
MSKenv_t env = NULL;
MSKtask_t task = NULL;
MSKint64t zeroDom, quadDom;
/* Input data dimensions */
const MSKint32t n = 3,
k = 2;
/* Create the mosek environment. */
r = MSK_makeenv(&env, NULL);
if (r == MSK_RES_OK)
{
/* Create the optimization task. */
r = MSK_maketask(env, 0, 0, &task);
if (r == MSK_RES_OK)
{
MSK_linkfunctotaskstream(task, MSK_STREAM_LOG, NULL, printstr);
/* Create n free variables */
if (r == MSK_RES_OK)
r = MSK_appendvars(task, n);
if (r == MSK_RES_OK)
r = MSK_putvarboundsliceconst(task, 0, n, MSK_BK_FR, -MSK_INFINITY, +MSK_INFINITY);
/* Set up the objective */
{
double c[] = {2.0, 3.0, -1.0};
if (r == MSK_RES_OK)
r = MSK_putcslice(task, 0, n, c);
if (r == MSK_RES_OK)
r = MSK_putobjsense(task, MSK_OBJECTIVE_SENSE_MAXIMIZE);
}
{
/* Set AFE rows representing the linear constraint */
if (r == MSK_RES_OK)
r = MSK_appendafes(task, 1);
for(i = 0; i < n && r == MSK_RES_OK; i++)
r = MSK_putafefentry(task, 0, i, 1.0);
if (r == MSK_RES_OK)
r = MSK_putafeg(task, 0, -1.0);
}
{
/* Set AFE rows representing the quadratic constraint */
/* F matrix data in sparse form */
MSKint64t Fsubi[] = {2, 2, 3, 3}; /* G is placed from row 2 of F */
MSKint32t Fsubj[] = {0, 1, 0, 2};
double Fval[] = {1.5, 0.1, 0.3, 2.1};
int numEntries = 4;
/* Other data */
double h[] = {0, 0.1};
double gamma = 0.03;
if (r == MSK_RES_OK)
r = MSK_appendafes(task, k + 1);
if (r == MSK_RES_OK)
r = MSK_putafefentrylist(task, numEntries, Fsubi, Fsubj, Fval);
if (r == MSK_RES_OK)
r = MSK_putafeg(task, 1, gamma);
if (r == MSK_RES_OK)
r = MSK_putafegslice(task, 2, k+2, h);
}
/* Define a conic quadratic domain */
if (r == MSK_RES_OK)
r = MSK_appendrzerodomain(task, 1, &zeroDom);
if (r == MSK_RES_OK)
r = MSK_appendquadraticconedomain(task, k + 1, &quadDom);
/* Append affine conic constraints */
{
/* Linear constraint */
MSKint64t afeidx[] = {0};
if (r == MSK_RES_OK)
r = MSK_appendacc(task,
zeroDom, /* Domain index */
1, /* Dimension */
afeidx, /* Indices of AFE rows */
NULL); /* Ignored */
}
{
/* Quadratic constraint */
MSKint64t afeidx[] = {1, 2, 3};
if (r == MSK_RES_OK)
r = MSK_appendacc(task,
quadDom, /* Domain index */
k + 1, /* Dimension */
afeidx, /* Indices of AFE rows */
NULL); /* Ignored */
}
/* Begin optimization and fetching the solution */
if (r == MSK_RES_OK)
{
MSKrescodee trmcode;
/* Run optimizer */
r = MSK_optimizetrm(task, &trmcode);
/* Print a summary containing information
about the solution for debugging purposes*/
MSK_solutionsummary(task, MSK_STREAM_MSG);
if (r == MSK_RES_OK)
{
MSKsolstae solsta;
MSK_getsolsta(task, MSK_SOL_ITR, &solsta);
MSK_getsolsta(task, MSK_SOL_ITR, &solsta);
switch (solsta)
{
case MSK_SOL_STA_OPTIMAL:
{
double *xx, *doty, *activity = NULL;
/* Fetch the primal solution */
xx = calloc(n, sizeof(double));
MSK_getxx(task,
MSK_SOL_ITR, /* Request the interior solution. */
xx);
printf("Optimal primal solution\n");
for (j = 0; j < n; ++j)
printf("x[%d]: %e\n", j, xx[j]);
free(xx);
/* Fetch the dual doty solution for the ACC */
doty = calloc(k + 1, sizeof(double));
MSK_getaccdoty(task,
MSK_SOL_ITR, /* Request the interior solution. */
1, /* ACC index of quadratic ACC. */
doty);
printf("Dual doty of the quadratic ACC\n");
for (j = 0; j < k + 1; ++j)
printf("doty[%d]: %e\n", j, doty[j]);
free(doty);
/* Fetch the activity of the ACC */
activity = calloc(k + 1, sizeof(double));
MSK_evaluateacc(task,
MSK_SOL_ITR, /* Request the interior solution. */
0, /* ACC index. */
activity);
printf("Activity of the ACC\n");
for (j = 0; j < k + 1; ++j)
printf("activity[%d]: %e\n", j, activity[j]);
free(activity);
}
break;
case MSK_SOL_STA_DUAL_INFEAS_CER:
case MSK_SOL_STA_PRIM_INFEAS_CER:
printf("Primal or dual infeasibility certificate found.\n");
break;
case MSK_SOL_STA_UNKNOWN:
printf("The status of the solution could not be determined. Termination code: %d.\n", trmcode);
break;
default:
printf("Other solution status.");
break;
}
}
else
{
printf("Error while optimizing.\n");
}
}
if (r != MSK_RES_OK)
{
/* In case of an error print error code and description. */
char symname[MSK_MAX_STR_LEN];
char desc[MSK_MAX_STR_LEN];
printf("An error occurred while optimizing.\n");
MSK_getcodedesc(r,
symname,
desc);
printf("Error %s - '%s'\n", symname, desc);
}
}
/* Delete the task and the associated data. */
MSK_deletetask(&task);
}
/* Delete the environment and the associated data. */
MSK_deleteenv(&env);
return (r);
} /* main */
blas_lapack.c
/*
Copyright: Copyright (c) MOSEK ApS, Denmark. All rights reserved.
File: blas_lapack.c
Purpose: To demonstrate how to call BLAS/LAPACK routines for
which MOSEK provides simplified interfaces.
*/
#include "mosek.h"
void print_matrix(MSKrealt* x, MSKint32t r, MSKint32t c)
{
MSKint32t i, j;
for (i = 0; i < r; i++)
{
for (j = 0; j < c; j++)
printf("%f ", x[j * r + i]);
printf("\n");
}
}
int main(int argc, char* argv[])
{
MSKrescodee r = MSK_RES_OK;
MSKenv_t env = NULL;
const MSKint32t n = 3, m = 2, k = 3;
MSKrealt alpha = 2.0, beta = 0.5;
MSKrealt x[] = {1.0, 1.0, 1.0};
MSKrealt y[] = {1.0, 2.0, 3.0};
MSKrealt z[] = {1.0, 1.0};
MSKrealt A[] = {1.0, 1.0, 2.0, 2.0, 3.0, 3.0};
MSKrealt B[] = {1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0};
MSKrealt C[] = {1.0, 2.0, 3.0, 4.0, 5.0, 6.0};
MSKrealt D[] = {1.0, 1.0, 1.0, 1.0};
MSKrealt Q[] = {1.0, 0.0, 0.0, 2.0};
MSKrealt v[] = {0.0, 0.0, 0.0};
MSKrealt xy;
/* BLAS routines*/
r = MSK_makeenv(&env, NULL);
printf("n=%d m=%d k=%d\n", m, n, k);
printf("alpha=%f\n", alpha);
printf("beta=%f\n", beta);
r = MSK_dot(env, n, x, y, &xy);
printf("dot results= %f r=%d\n", xy, r);
print_matrix(x, 1, n);
print_matrix(y, 1, n);
r = MSK_axpy(env, n, alpha, x, y);
puts("axpy results is");
print_matrix(y, 1, n);
r = MSK_gemv(env, MSK_TRANSPOSE_NO, m, n, alpha, A, x, beta, z);
printf("gemv results is (r=%d) \n", r);
print_matrix(z, 1, m);
r = MSK_gemm(env, MSK_TRANSPOSE_NO, MSK_TRANSPOSE_NO, m, n, k, alpha, A, B, beta, C);
printf("gemm results is (r=%d) \n", r);
print_matrix(C, m, n);
r = MSK_syrk(env, MSK_UPLO_LO, MSK_TRANSPOSE_NO, m, k, 1., A, beta, D);
printf("syrk results is (r=%d) \n", r);
print_matrix(D, m, m);
/* LAPACK routines*/
r = MSK_potrf(env, MSK_UPLO_LO, m, Q);
printf("potrf results is (r=%d) \n", r);
print_matrix(Q, m, m);
r = MSK_syeig(env, MSK_UPLO_LO, m, Q, v);
printf("syeig results is (r=%d) \n", r);
print_matrix(v, 1, m);
r = MSK_syevd(env, MSK_UPLO_LO, m, Q, v);
printf("syevd results is (r=%d) \n", r);
print_matrix(v, 1, m);
print_matrix(Q, m, m);
/* Delete the environment and the associated data. */
MSK_deleteenv(&env);
return r;
}
callback.c
/*
Copyright: Copyright (c) MOSEK ApS, Denmark. All rights reserved.
File: callback.c
Purpose: To demonstrate how to use the progress
callback.
Compile and link the file with MOSE, then
use as follows:
callback psim 25fv47.mps
callback dsim 25fv47.mps
callback intpnt 25fv47.mps
The first argument tells which optimizer to use
i.e. psim is primal simplex, dsim is dual simplex
and intpnt is interior-point.
*/
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include "mosek.h"
#define CONT_EXAMPLE
/* Type of user data used in callback functions */
typedef struct {
double maxtime; // Time limit for the optimizer
int numvars;
double *xx; // For storing the integer solution when mixed integer optimizer is used
} cbdata;
typedef cbdata* cbdata_t;
/* Note: This function is declared using MSKAPI,
so the correct calling convention is
employed. */
static int MSKAPI usercallback(MSKtask_t task,
MSKuserhandle_t handle,
MSKcallbackcodee caller,
const MSKrealt * douinf,
const MSKint32t * intinf,
const MSKint64t * lintinf)
{
cbdata_t data = (cbdata_t) handle;
double maxtime = data->maxtime;
MSKrescodee r;
switch (caller)
{
case MSK_CALLBACK_BEGIN_INTPNT:
printf("Starting interior-point optimizer\n");
break;
case MSK_CALLBACK_INTPNT:
printf("Iterations: %-3d Time: %6.2f(%.2f) ",
intinf[MSK_IINF_INTPNT_ITER],
douinf[MSK_DINF_OPTIMIZER_TIME],
douinf[MSK_DINF_INTPNT_TIME]);
printf("Primal obj.: %-18.6e Dual obj.: %-18.6e\n",
douinf[MSK_DINF_INTPNT_PRIMAL_OBJ],
douinf[MSK_DINF_INTPNT_DUAL_OBJ]);
break;
case MSK_CALLBACK_END_INTPNT:
printf("Interior-point optimizer finished.\n");
break;
case MSK_CALLBACK_BEGIN_PRIMAL_SIMPLEX:
printf("Primal simplex optimizer started.\n");
break;
case MSK_CALLBACK_UPDATE_PRIMAL_SIMPLEX:
printf("Iterations: %-3d ",
intinf[MSK_IINF_SIM_PRIMAL_ITER]);
printf(" Elapsed time: %6.2f(%.2f)\n",
douinf[MSK_DINF_OPTIMIZER_TIME],
douinf[MSK_DINF_SIM_TIME]);
printf("Obj.: %-18.6e\n",
douinf[MSK_DINF_SIM_OBJ]);
break;
case MSK_CALLBACK_END_PRIMAL_SIMPLEX:
printf("Primal simplex optimizer finished.\n");
break;
case MSK_CALLBACK_BEGIN_DUAL_SIMPLEX:
printf("Dual simplex optimizer started.\n");
break;
case MSK_CALLBACK_UPDATE_DUAL_SIMPLEX:
printf("Iterations: %-3d ", intinf[MSK_IINF_SIM_DUAL_ITER]);
printf(" Elapsed time: %6.2f(%.2f)\n",
douinf[MSK_DINF_OPTIMIZER_TIME],
douinf[MSK_DINF_SIM_TIME]);
printf("Obj.: %-18.6e\n", douinf[MSK_DINF_SIM_OBJ]);
break;
case MSK_CALLBACK_END_DUAL_SIMPLEX:
printf("Dual simplex optimizer finished.\n");
break;
case MSK_CALLBACK_NEW_INT_MIO:
printf("New integer solution has been located.\n");
r = MSK_getxx(task, MSK_SOL_ITG, data->xx);
if (r == MSK_RES_OK) {
int i;
printf("xx = ");
for (i = 0; i < data->numvars; i++) printf("%lf ", data->xx[i]);
printf("\nObj.: %f\n", douinf[MSK_DINF_MIO_OBJ_INT]);
}
default:
break;
}
if (douinf[MSK_DINF_OPTIMIZER_TIME] >= maxtime)
{
/* mosek is spending too much time.
Terminate it. */
return (1);
}
return (0);
} /* usercallback */
static void MSKAPI printtxt(void *info,
const char *buffer)
{ printf("%s", buffer);
} /* printtxt */
int main(int argc, const char *argv[])
{
double maxtime,
*xx, *y;
MSKrescodee r, trmr;
int j, i, numcon, numvar;
FILE *f;
MSKenv_t env;
MSKtask_t task;
cbdata data;
#ifdef MIO_EXAMPLE
/* To test the mixed-integer solution callback. */
const char * slvr = "";
const char * filename = "../data/milo1.lp";
#endif
#ifdef CONT_EXAMPLE
/* To test interior-point/simplex optimizers on continuous problems */
const char * slvr = "intpnt";
const char * filename = "../data/25fv47.mps";
#endif
printf("callback example\n");
if (argc < 3)
{
printf("Usage: callback ( psim | dsim | intpnt ) filename\n");
if (argc == 2)
slvr = argv[1];
}
else
{
slvr = argv[1];
filename = argv[2];
}
/* Create mosek environment. */
/* "" should be replaced by NULL in a NON DEBUG setting. */
r = MSK_makeenv(&env, "");
/* Check the return code. */
if (r == MSK_RES_OK)
{
/* Create an (empty) optimization task. */
r = MSK_makeemptytask(env, &task);
if (r == MSK_RES_OK)
{
MSK_linkfunctotaskstream(task, MSK_STREAM_MSG, NULL, printtxt);
MSK_linkfunctotaskstream(task, MSK_STREAM_ERR, NULL, printtxt);
}
/* Specifies that data should be read from the file.
*/
if (r == MSK_RES_OK)
r = MSK_readdata(task, filename);
if (r == MSK_RES_OK)
{
if (0 == strcmp(slvr, "psim"))
MSK_putintparam(task, MSK_IPAR_OPTIMIZER, MSK_OPTIMIZER_PRIMAL_SIMPLEX);
else if (0 == strcmp(slvr, "dsim"))
MSK_putintparam(task, MSK_IPAR_OPTIMIZER, MSK_OPTIMIZER_DUAL_SIMPLEX);
else if (0 == strcmp(slvr, "intpnt"))
MSK_putintparam(task, MSK_IPAR_OPTIMIZER, MSK_OPTIMIZER_INTPNT);
/* Tell mosek about the call-back function. */
data.maxtime = 0.05;
MSK_getnumvar(task, &data.numvars);
data.xx = MSK_callocenv(env, data.numvars, sizeof(double));
MSK_putcallbackfunc(task,
usercallback,
(void *) &data);
/* Turn all MOSEK logging off. */
MSK_putintparam(task,
MSK_IPAR_LOG,
0);
r = MSK_optimizetrm(task, &trmr);
printf("Return code - %d, termination code - %d\n", r, trmr);
MSK_solutionsummary(task, MSK_STREAM_MSG);
MSK_freeenv(env, data.xx);
}
{
MSKrescodee lr = MSK_deletetask(&task);
if ( r==MSK_RES_OK )
r = lr;
}
}
{
MSKrescodee lr=MSK_deleteenv(&env);;
if ( r==MSK_RES_OK )
r = lr;
}
printf("Return code - %d\n", r);
return (0);
} /* main */
ceo1.c
/*
Copyright: Copyright (c) MOSEK ApS, Denmark. All rights reserved.
File: ceo1.c
Purpose: To demonstrate how to solve a small conic exponential
optimization problem using the MOSEK API.
*/
#include <stdio.h>
#include "mosek.h" /* Include the MOSEK definition file. */
static void MSKAPI printstr(void *handle,
const char str[])
{
printf("%s", str);
} /* printstr */
int main(int argc, const char *argv[])
{
MSKrescodee r;
const MSKint32t numvar = 3,
numcon = 1;
const MSKint64t numafe = 3,
f_nnz = 3;
MSKboundkeye bkc = MSK_BK_FX;
double blc = 1.0;
double buc = 1.0;
MSKboundkeye bkx[] = {MSK_BK_FR,
MSK_BK_FR,
MSK_BK_FR
};
double blx[] = {-MSK_INFINITY,
-MSK_INFINITY,
-MSK_INFINITY
};
double bux[] = { +MSK_INFINITY,
+MSK_INFINITY,
+MSK_INFINITY
};
double c[] = {1.0,
1.0,
0.0
};
double a[] = {1.0, 1.0, 1.0};
MSKint32t asub[] = {0, 1, 2};
MSKint64t afeidx[] = {0, 1, 2};
MSKint32t varidx[] = {0, 1, 2};
MSKrealt f_val[] = {1, 1, 1};
MSKint64t domidx = 0;
MSKint32t i, j, csub[3];
MSKenv_t env = NULL;
MSKtask_t task = NULL;
/* Create the mosek environment. */
r = MSK_makeenv(&env, NULL);
if (r == MSK_RES_OK)
{
/* Create the optimization task. */
r = MSK_maketask(env, numcon, numvar, &task);
if (r == MSK_RES_OK)
{
MSK_linkfunctotaskstream(task, MSK_STREAM_LOG, NULL, printstr);
/* Append 'numcon' empty constraints.
The constraints will initially have no bounds. */
if (r == MSK_RES_OK)
r = MSK_appendcons(task, numcon);
/* Append 'numvar' variables.
The variables will initially be fixed at zero (x=0). */
if (r == MSK_RES_OK)
r = MSK_appendvars(task, numvar);
/* Append 'numafe' affine expressions.
The affine expressions will initially be empty. */
if (r == MSK_RES_OK)
r = MSK_appendafes(task, numafe);
/* Set up the linear part */
if (r == MSK_RES_OK)
r = MSK_putcslice(task, 0, numvar, c);
if (r == MSK_RES_OK)
r = MSK_putarow(task, 0, numvar, asub, a);
if (r == MSK_RES_OK)
r = MSK_putconbound(task, 0, bkc, blc, buc);
if (r == MSK_RES_OK)
r = MSK_putvarboundslice(task, 0, numvar, bkx, blx, bux);
if (r == MSK_RES_OK)
{
r = MSK_putafefentrylist(task, f_nnz, afeidx, varidx, f_val);
if (r == MSK_RES_OK)
r = MSK_appendprimalexpconedomain(task, &domidx);
if (r == MSK_RES_OK)
r = MSK_appendaccseq(task, domidx, numafe, 0, NULL);
}
if (r == MSK_RES_OK)
{
MSKrescodee trmcode;
/* Run optimizer */
r = MSK_optimizetrm(task, &trmcode);
/* Print a summary containing information
about the solution for debugging purposes*/
MSK_solutionsummary(task, MSK_STREAM_MSG);
if (r == MSK_RES_OK)
{
MSKsolstae solsta;
MSK_getsolsta(task, MSK_SOL_ITR, &solsta);
switch (solsta)
{
case MSK_SOL_STA_OPTIMAL:
{
double *xx = NULL;
xx = calloc(numvar, sizeof(double));
if (xx)
{
MSK_getxx(task,
MSK_SOL_ITR, /* Request the interior solution. */
xx);
printf("Optimal primal solution\n");
for (j = 0; j < numvar; ++j)
printf("x[%d]: %e\n", j, xx[j]);
}
else
{
r = MSK_RES_ERR_SPACE;
}
free(xx);
}
break;
case MSK_SOL_STA_DUAL_INFEAS_CER:
case MSK_SOL_STA_PRIM_INFEAS_CER:
printf("Primal or dual infeasibility certificate found.\n");
break;
case MSK_SOL_STA_UNKNOWN:
printf("The status of the solution could not be determined. Termination code: %d.\n", trmcode);
break;
default:
printf("Other solution status.");
break;
}
}
else
{
printf("Error while optimizing.\n");
}
}
if (r != MSK_RES_OK)
{
/* In case of an error print error code and description. */
char symname[MSK_MAX_STR_LEN];
char desc[MSK_MAX_STR_LEN];
printf("An error occurred while optimizing.\n");
MSK_getcodedesc(r,
symname,
desc);
printf("Error %s - '%s'\n", symname, desc);
}
}
/* Delete the task and the associated data. */
MSK_deletetask(&task);
}
/* Delete the environment and the associated data. */
MSK_deleteenv(&env);
return (r);
} /* main */
concurrent1.cc
/*
Copyright: Copyright (c) MOSEK ApS, Denmark. All rights reserved.
File: concurrent1.cc
Purpose: Demonstrates a simple implementation of a concurrent optimizer.
The concurrent optimizer starts a few parallel optimizations
of the same problem using different algorithms, and reports
a solution when the first optimizer is ready.
This example also demonstrates how to define a simple callback handler
that stops the optimizer when requested.
For cross-platform compatibility this is C++ code requiring C++11.
This is due to the use of std::thread. The rest is pure C. It should be easily
adapted to C and any threading model by only modifying the "optimize"
function.
*/
#include<stdio.h>
#include<stdlib.h>
#include<mosek.h>
#include<thread>
/* This function prints log output from MOSEK to the terminal. */
static void MSKAPI printstr(void *handle,
const char str[])
{
printf("%s", str);
}
/**
Defines a Mosek callback function whose only function
is to indicate if the optimizer should be stopped.
*/
int stop = 0;
int firstStop = -1;
MSKint32t MSKAPI callback (MSKtask_t task, MSKuserhandle_t usrptr, MSKcallbackcodee caller,
const MSKrealt * douinf, const MSKint32t * intinf, const MSKint64t * lintinf)
{
return stop;
}
/** Takes a list of tasks and optimizes then in parallel. The
response code and termination code from each optimization is
stored in ``res`` and ``trm``.
When one task completes with rescode == ok, others are terminated.
Returns the index of the first optimizer which returned without error.
Whether or not this is the task firstOK contains the
most valuable answer, is for the caller to decide.
Otherwise returns -1.
*/
void runTask(int num,
MSKtask_t task,
MSKrescodee *res,
MSKrescodee *trm)
{
*res = MSK_optimizetrm(task, trm);
if (*res == MSK_RES_OK) {
if (!stop) firstStop = num;
stop = 1;
}
}
int optimize(int n,
MSKtask_t *tasks,
MSKrescodee *res,
MSKrescodee *trm)
{
int i;
std::thread * jobs = new std::thread[n];
// Set a callback function and start optimization
for(i = 0; i < n; ++i) {
MSK_putcallbackfunc(tasks[i], callback, NULL);
res[i] = trm[i] = MSK_RES_ERR_UNKNOWN;
jobs[i] = std::thread(runTask, i, tasks[i], &(res[i]), &(trm[i]));
}
// Join all threads
for(i = 0; i < n; ++i) jobs[i].join();
delete[] jobs;
// For debugging, print res and trm codes for all optimizers
for(i = 0; i < n; ++i)
printf("Optimizer %d res %d trm %d\n", i, res[i], trm[i]);
return firstStop;
}
/**
Given a continuous task, set up jobs to optimize it
with a list of different solvers.
Returns an index, corresponding to the optimization
task that is returned as winTask. This is the task
with the best possible status of those that finished.
If none task is considered successfull returns -1.
*/
int optimizeconcurrent(MSKtask_t task,
int n,
MSKoptimizertypee *optimizers,
MSKtask_t *winTask,
MSKrescodee *winTrm,
MSKrescodee *winRes)
{
MSKtask_t *tasks = new MSKtask_t[n];
MSKrescodee *res = new MSKrescodee[n];
MSKrescodee *trm = new MSKrescodee[n];
// Clone tasks and choose various optimizers
for (int i = 0; i < n; ++i)
{
MSK_clonetask(task, &(tasks[i]));
MSK_putintparam(tasks[i], MSK_IPAR_OPTIMIZER, optimizers[i]);
}
// Solve tasks in parallel
int firstOK = optimize(n, tasks, res, trm);
if (firstOK >= 0)
{
*winTask = tasks[firstOK];
*winTrm = trm[firstOK];
*winRes = res[firstOK];
}
else
{
*winTask = NULL;
*winTrm = MSK_RES_ERR_UNKNOWN;
*winRes = MSK_RES_ERR_UNKNOWN;
}
// Cleanup
for (int i = 0; i < n; ++i)
if (i != firstOK) MSK_deletetask(&(tasks[i]));
delete[] tasks; delete[] res; delete[] trm;
return firstOK;
}
/**
Given a mixed-integer task, set up jobs to optimize it
with different values of seed. That will lead to
different execution paths of the optimizer.
Returns an index, corresponding to the optimization
task that is returned as winTask. This is the task
with the best value of the objective function.
If none task is considered successful returns -1.
Typically, the input task would contain a time limit. The two
major scenarios are:
1. Some clone ends before time limit - then it has optimum.
2. All clones reach time limit - pick the one with best objective.
*/
int optimizeconcurrentMIO(MSKtask_t task,
int n,
int *seeds,
MSKtask_t *winTask,
MSKrescodee *winTrm,
MSKrescodee *winRes)
{
MSKtask_t *tasks = new MSKtask_t[n];
MSKrescodee *res = new MSKrescodee[n];
MSKrescodee *trm = new MSKrescodee[n];
*winTask = NULL;
*winTrm = MSK_RES_ERR_UNKNOWN;
*winRes = MSK_RES_ERR_UNKNOWN;
int bestPos = -1;
// Clone tasks and choose various optimizers
for (int i = 0; i < n; ++i)
{
MSK_clonetask(task, &(tasks[i]));
MSK_putintparam(tasks[i], MSK_IPAR_MIO_SEED, seeds[i]);
}
// Solve tasks in parallel
int firstOK = optimize(n, tasks, res, trm);
if (firstOK >= 0)
{
// Pick the task that ended with res = ok
// and contains an integer solution with best objective value
MSKobjsensee sense;
double bestObj;
MSK_getobjsense(task, &sense);
bestObj = (sense == MSK_OBJECTIVE_SENSE_MINIMIZE) ? 1.0e+10 : -1.0e+10;
for (int i = 0; i < n; ++i) {
double priObj;
MSK_getprimalobj(tasks[i], MSK_SOL_ITG, &priObj);
printf("%d %f\n", i, priObj);
}
for (int i = 0; i < n; ++i) {
double priObj;
MSKsolstae solsta;
MSK_getprimalobj(tasks[i], MSK_SOL_ITG, &priObj);
MSK_getsolsta(tasks[i], MSK_SOL_ITG, &solsta);
if ((res[i] == MSK_RES_OK) &&
(solsta == MSK_SOL_STA_PRIM_FEAS ||
solsta == MSK_SOL_STA_INTEGER_OPTIMAL) &&
((sense == MSK_OBJECTIVE_SENSE_MINIMIZE) ?
(priObj < bestObj) : (priObj > bestObj) ) )
{
bestObj = priObj;
bestPos = i;
}
}
if (bestPos != -1)
{
*winTask = tasks[bestPos];
*winTrm = trm[bestPos];
*winRes = res[bestPos];
}
}
// Cleanup
for (int i = 0; i < n; ++i)
if (i != bestPos) MSK_deletetask(&(tasks[i]));
delete[] tasks; delete[] res; delete[] trm;
return bestPos;
}
/**
This is an example of how one can use the methods
optimizeconcurrent
optimizeconcurrentMIO
argv[0] : name of file with input problem
argv[1]: (optional) time limit
*/
int main(int argc, char **argv)
{
MSKenv_t env;
MSKtask_t task;
int numint;
MSKtask_t t;
MSKrescodee res, trm;
int idx;
MSK_makeenv(&env, NULL);
MSK_makeemptytask(env, &task);
if (argc >= 2)
MSK_readdata(task, argv[1]);
else
MSK_readdata(task, "../data/25fv47.mps");
if (argc >= 3)
MSK_putdouparam(task, MSK_DPAR_OPTIMIZER_MAX_TIME, atof(argv[2]));
MSK_getnumintvar(task, &numint);
if (numint == 0)
{
/* If the problem is continuous
optimize it with three continuous optimizers.
(Simplex will fail for non-linear problems)
*/
MSKoptimizertypee optimizers[3] = {
MSK_OPTIMIZER_CONIC,
MSK_OPTIMIZER_DUAL_SIMPLEX,
MSK_OPTIMIZER_PRIMAL_SIMPLEX
};
idx = optimizeconcurrent(task, 3, optimizers, &t, &trm, &res);
}
else
{
/* Mixed-integer problem.
Try various seeds.
*/
int seeds[3] = { 42, 13, 71749373 };
idx = optimizeconcurrentMIO(task, 3, seeds, &t, &trm, &res);
}
// Check results and print the best answer
if (idx >= 0)
{
printf("Result from optimizer with index %d: res %d trm %d\n", idx, res, trm);
MSK_linkfunctotaskstream(t, MSK_STREAM_LOG, NULL, printstr);
MSK_optimizersummary(t, MSK_STREAM_LOG);
MSK_solutionsummary(t, MSK_STREAM_LOG);
MSK_deletetask(&t);
}
else
{
printf("All optimizers failed.");
}
MSK_deletetask(&task);
MSK_deleteenv(&env);
return 0;
}
cqo1.c
/*
Copyright: Copyright (c) MOSEK ApS, Denmark. All rights reserved.
File: cqo1.c
Purpose: To demonstrate how to solve a small conic quadratic
optimization problem using the MOSEK API.
*/
#include <stdio.h>
#include "mosek.h" /* Include the MOSEK definition file. */
static void MSKAPI printstr(void *handle,
const char str[])
{
printf("%s", str);
} /* printstr */
int main(int argc, const char *argv[])
{
MSKrescodee r;
const MSKint32t numvar = 6,
numcon = 1;
const MSKint64t numafe = 6,
numacc = 2,
f_nnz = 6;
MSKboundkeye bkc[] = { MSK_BK_FX };
double blc[] = { 1.0 };
double buc[] = { 1.0 };
MSKboundkeye bkx[] = {MSK_BK_LO,
MSK_BK_LO,
MSK_BK_LO,
MSK_BK_FR,
MSK_BK_FR,
MSK_BK_FR
};
double blx[] = {0.0,
0.0,
0.0,
-MSK_INFINITY,
-MSK_INFINITY,
-MSK_INFINITY
};
double bux[] = { +MSK_INFINITY,
+MSK_INFINITY,
+MSK_INFINITY,
+MSK_INFINITY,
+MSK_INFINITY,
+MSK_INFINITY
};
double c[] = {0.0,
0.0,
0.0,
1.0,
1.0,
1.0
};
MSKint32t aptrb[] = {0, 1, 2, 3, 3, 3},
aptre[] = {1, 2, 3, 3, 3, 3},
asub[] = {0, 0, 0, 0};
double aval[] = {1.0, 1.0, 2.0};
MSKint64t afeidx[] = {0, 1, 2, 3, 4, 5};
MSKint32t varidx[] = {3, 0, 1, 4, 5, 2};
MSKrealt f_val[] = {1, 1, 1, 1, 1, 1};
MSKint64t domidx[] = {0, 0};
MSKint32t i, j, csub[3];
MSKenv_t env = NULL;
MSKtask_t task = NULL;
/* Create the mosek environment. */
r = MSK_makeenv(&env, NULL);
if (r == MSK_RES_OK)
{
/* Create the optimization task. */
r = MSK_maketask(env, numcon, numvar, &task);
if (r == MSK_RES_OK)
{
MSK_linkfunctotaskstream(task, MSK_STREAM_LOG, NULL, printstr);
/* Append 'numcon' empty constraints.
The constraints will initially have no bounds. */
if (r == MSK_RES_OK)
r = MSK_appendcons(task, numcon);
/* Append 'numvar' variables.
The variables will initially be fixed at zero (x=0). */
if (r == MSK_RES_OK)
r = MSK_appendvars(task, numvar);
/* Append 'numafe' affine expressions.
The affine expressions will initially be empty. */
if (r == MSK_RES_OK)
r = MSK_appendafes(task, numafe);
for (j = 0; j < numvar && r == MSK_RES_OK; ++j)
{
/* Set the linear term c_j in the objective.*/
if (r == MSK_RES_OK)
r = MSK_putcj(task, j, c[j]);
/* Set the bounds on variable j.
blx[j] <= x_j <= bux[j] */
if (r == MSK_RES_OK)
r = MSK_putvarbound(task,
j, /* Index of variable.*/
bkx[j], /* Bound key.*/
blx[j], /* Numerical value of lower bound.*/
bux[j]); /* Numerical value of upper bound.*/
/* Input column j of A */
if (r == MSK_RES_OK)
r = MSK_putacol(task,
j, /* Variable (column) index.*/
aptre[j] - aptrb[j], /* Number of non-zeros in column j.*/
asub + aptrb[j], /* Pointer to row indexes of column j.*/
aval + aptrb[j]); /* Pointer to Values of column j.*/
}
/* Set the bounds on constraints.
for i=1, ...,numcon : blc[i] <= constraint i <= buc[i] */
for (i = 0; i < numcon && r == MSK_RES_OK; ++i)
r = MSK_putconbound(task,
i, /* Index of constraint.*/
bkc[i], /* Bound key.*/
blc[i], /* Numerical value of lower bound.*/
buc[i]); /* Numerical value of upper bound.*/
if (r == MSK_RES_OK)
{
/* Set the non-zero entries of the F matrix */
r = MSK_putafefentrylist(task, f_nnz, afeidx, varidx, f_val);
/* Append quadratic cone domain */
if (r == MSK_RES_OK)
r = MSK_appendquadraticconedomain(task, 3, domidx);
/* Append rotated quadratic cone domain */
if (r == MSK_RES_OK)
r = MSK_appendrquadraticconedomain(task, 3, domidx+1);
/* Append two ACCs made up of the AFEs and the domains defined above. */
if (r == MSK_RES_OK)
r = MSK_appendaccsseq(task, numacc, domidx, numafe, afeidx[0], NULL);
}
if (r == MSK_RES_OK)
{
MSKrescodee trmcode;
/* Run optimizer */
r = MSK_optimizetrm(task, &trmcode);
/* Print a summary containing information
about the solution for debugging purposes*/
MSK_solutionsummary(task, MSK_STREAM_MSG);
if (r == MSK_RES_OK)
{
MSKsolstae solsta;
MSK_getsolsta(task, MSK_SOL_ITR, &solsta);
switch (solsta)
{
case MSK_SOL_STA_OPTIMAL:
{
double *xx = NULL;
xx = calloc(numvar, sizeof(double));
if (xx)
{
MSK_getxx(task,
MSK_SOL_ITR, /* Request the interior solution. */
xx);
printf("Optimal primal solution\n");
for (j = 0; j < numvar; ++j)
printf("x[%d]: %e\n", j, xx[j]);
}
else
{
r = MSK_RES_ERR_SPACE;
}
free(xx);
}
break;
case MSK_SOL_STA_DUAL_INFEAS_CER:
case MSK_SOL_STA_PRIM_INFEAS_CER:
printf("Primal or dual infeasibility certificate found.\n");
break;
case MSK_SOL_STA_UNKNOWN:
printf("The status of the solution could not be determined. Termination code: %d.\n", trmcode);
break;
default:
printf("Other solution status.");
break;
}
}
else
{
printf("Error while optimizing.\n");
}
}
if (r != MSK_RES_OK)
{
/* In case of an error print error code and description. */
char symname[MSK_MAX_STR_LEN];
char desc[MSK_MAX_STR_LEN];
printf("An error occurred while optimizing.\n");
MSK_getcodedesc(r,
symname,
desc);
printf("Error %s - '%s'\n", symname, desc);
}
}
/* Delete the task and the associated data. */
MSK_deletetask(&task);
}
/* Delete the environment and the associated data. */
MSK_deleteenv(&env);
return (r);
} /* main */
djc1.c
////
// Copyright: Copyright (c) MOSEK ApS, Denmark. All rights reserved.
//
// File: djc1.c
//
// Purpose: Demonstrates how to solve the problem with two disjunctions:
//
// minimize 2x0 + x1 + 3x2 + x3
// subject to x0 + x1 + x2 + x3 >= -10
// (x0-2x1<=-1 and x2=x3=0) or (x2-3x3<=-2 and x1=x2=0)
// x0=2.5 or x1=2.5 or x2=2.5 or x3=2.5
////
#include <stdio.h>
#include "mosek.h"
/* This function prints log output from MOSEK to the terminal. */
static void MSKAPI printstr(void *handle,
const char str[])
{
printf("%s", str);
} /* printstr */
int main(int argc, const char *argv[])
{
MSKenv_t env = NULL;
MSKtask_t task = NULL;
MSKrescodee r = MSK_RES_OK;
MSKint32t i, j, numvar;
MSKint64t k, l, numafe, numdjc;
MSKint64t zero1, zero2, rminus1; // Domain indices
/* Create the mosek environment. */
r = MSK_makeenv(&env, NULL);
if (r == MSK_RES_OK)
{
/* Create the optimization task. */
r = MSK_maketask(env, 0, 0, &task);
if (r == MSK_RES_OK)
{
// Append free variables
numvar = 4;
r = MSK_appendvars(task, numvar);
if (r == MSK_RES_OK)
MSK_putvarboundsliceconst(task, 0, numvar, MSK_BK_FR, -MSK_INFINITY, MSK_INFINITY);
}
if (r == MSK_RES_OK)
{
// The linear part: the linear constraint
const MSKint32t idx[] = {0, 1, 2, 3};
const MSKrealt val[] = {1, 1, 1, 1};
r = MSK_appendcons(task, 1);
if (r == MSK_RES_OK) MSK_putarow(task, 0, 4, idx, val);
if (r == MSK_RES_OK) MSK_putconbound(task, 0, MSK_BK_LO, -10.0, -10.0);
}
if (r == MSK_RES_OK)
{
// The linear part: objective
const MSKint32t idx[] = {0, 1, 2, 3};
const MSKrealt val[] = {2, 1, 3, 1};
r = MSK_putobjsense(task, MSK_OBJECTIVE_SENSE_MINIMIZE);
if (r == MSK_RES_OK) MSK_putclist(task, 4, idx, val);
}
// Fill in the affine expression storage F, g
if (r == MSK_RES_OK)
{
numafe = 10;
r = MSK_appendafes(task, numafe);
}
if (r == MSK_RES_OK)
{
const MSKint64t fafeidx[] = {0, 0, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9};
const MSKint32t fvaridx[] = {0, 1, 2, 3, 0, 1, 2, 3, 0, 1, 2, 3};
const MSKrealt fval[] = {1.0, -2.0, 1.0, -3.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0};
const MSKrealt g[] = {1.0, 2.0, 0.0, 0.0, 0.0, 0.0, -2.5, -2.5, -2.5, -2.5};
r = MSK_putafefentrylist(task, 12, fafeidx, fvaridx, fval);
if (r == MSK_RES_OK)
r = MSK_putafegslice(task, 0, numafe, g);
}
if (r == MSK_RES_OK)
{
// Create domains
MSK_appendrzerodomain(task, 1, &zero1);
MSK_appendrzerodomain(task, 2, &zero2);
MSK_appendrminusdomain(task, 1, &rminus1);
}
if (r == MSK_RES_OK)
{
// Append disjunctive constraints
numdjc = 2;
r = MSK_appenddjcs(task, numdjc);
}
if (r == MSK_RES_OK)
{
// First disjunctive constraint
const MSKint64t domidxlist[] = {rminus1, zero2, rminus1, zero2};
const MSKint64t afeidxlist[] = {0, 4, 5, 1, 2, 3};
const MSKint64t termsizelist[] = {2, 2};
r = MSK_putdjc(task,
0, // DJC index
4, domidxlist,
6, afeidxlist,
NULL, // Unused
2, termsizelist);
}
if (r == MSK_RES_OK)
{
// Second disjunctive constraint
const MSKint64t domidxlist[] = {zero1, zero1, zero1, zero1};
const MSKint64t afeidxlist[] = {6, 7, 8, 9};
const MSKint64t termsizelist[] = {1, 1, 1, 1};
r = MSK_putdjc(task,
1, // DJC index
4, domidxlist,
4, afeidxlist,
NULL, // Unused
4, termsizelist);
}
// Useful for debugging
if (r == MSK_RES_OK)
{
// Write a human-readable file
r = MSK_writedata(task, "djc.ptf");
// Directs the log task stream to the 'printstr' function.
if (r == MSK_RES_OK)
r = MSK_linkfunctotaskstream(task, MSK_STREAM_LOG, NULL, printstr);
}
// Solve the problem
if (r == MSK_RES_OK)
{
MSKrescodee trmcode;
r = MSK_optimizetrm(task, &trmcode);
/* Print a summary containing information
about the solution for debugging purposes. */
MSK_solutionsummary(task, MSK_STREAM_LOG);
if (r == MSK_RES_OK)
{
MSKsolstae solsta;
if (r == MSK_RES_OK)
r = MSK_getsolsta(task,
MSK_SOL_ITG,
&solsta);
switch (solsta)
{
case MSK_SOL_STA_INTEGER_OPTIMAL:
{
double *xx = (double*) calloc(numvar, sizeof(double));
if (xx)
{
MSK_getxx(task,
MSK_SOL_ITG,
xx);
printf("Optimal primal solution\n");
for (j = 0; j < numvar; ++j)
printf("x[%d]: %e\n", j, xx[j]);
free(xx);
}
else
r = MSK_RES_ERR_SPACE;
break;
}
default:
printf("Another solution status.\n");
break;
}
}
}
if (r != MSK_RES_OK)
{
/* In case of an error print error code and description. */
char symname[MSK_MAX_STR_LEN];
char desc[MSK_MAX_STR_LEN];
printf("An error occurred while optimizing.\n");
MSK_getcodedesc(r,
symname,
desc);
printf("Error %s - '%s'\n", symname, desc);
}
/* Delete the task and the associated data. */
MSK_deletetask(&task);
}
/* Delete the environment and the associated data. */
MSK_deleteenv(&env);
return r;
}
errorreporting.c
/*
Copyright: Copyright (c) MOSEK ApS, Denmark. All rights reserved.
File: errorreporting.c
Purpose: To demonstrate how the error reporting can be customized.
*/
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include "mosek.h"
static MSKrescodee MSKAPI handleresponse(MSKuserhandle_t handle,
MSKrescodee r,
const char msg[])
/* A custom response handler. */
{
/* Find out if we had an error or warning */
MSKrescodetypee rct;
MSK_getresponseclass(r, &rct);
if (r == MSK_RES_OK)
{
/* Do nothing */
}
else if (rct == MSK_RESPONSE_WRN)
{
printf("MOSEK reports warning number %d: %s\n", r, msg);
r = MSK_RES_OK;
}
else if (rct == MSK_RESPONSE_ERR)
{
printf("MOSEK reports error number %d: %s\n", r, msg);
}
else
{
printf("Unexpected response %d: %s\n", r, msg);
}
return (r);
} /* handlerespone */
int main(int argc, char *argv[])
{
MSKenv_t env;
MSKrescodee r;
MSKtask_t task;
r = MSK_makeenv(&env, NULL);
if (r == MSK_RES_OK)
{
r = MSK_makeemptytask(env, &task);
if (r == MSK_RES_OK)
{
/*
* Input a custom warning and error handler function.
*/
MSK_putresponsefunc(task, handleresponse, NULL);
/* User defined code goes here */
/* This will provoke an error */
if (r == MSK_RES_OK)
r = MSK_putaij(task, 10, 10, 1.0);
}
MSK_deletetask(&task);
}
MSK_deleteenv(&env);
printf("Return code - %d\n", r);
if (r == MSK_RES_ERR_INDEX_IS_TOO_LARGE)
return MSK_RES_OK;
else
return 1;
} /* main */
feasrepairex1.c
/*
Copyright: Copyright (c) MOSEK ApS, Denmark. All rights reserved.
File: feasrepairex1.c
Purpose: To demonstrate how to use the MSK_primalrepair function to
repair an infeasible problem.
*/
#include <math.h>
#include <stdio.h>
#include "mosek.h"
static void MSKAPI printstr(void *handle,
const char str[])
{
fputs(str, stdout);
} /* printstr */
static const char * feasrepair_lp =
"minimize \n"
" obj: - 10 x1 - 9 x2 \n"
"st \n"
" c1: + 7e-01 x1 + x2 <= 630 \n"
" c2: + 5e-01 x1 + 8.333333333e-01 x2 <= 600 \n"
" c3: + x1 + 6.6666667e-01 x2 <= 708 \n"
" c4: + 1e-01 x1 + 2.5e-01 x2 <= 135 \n"
"bounds \n"
"x2 >= 650 \n"
"end \n";
int main(int argc, const char *argv[])
{
MSKenv_t env;
MSKrescodee r, trmcode;
MSKtask_t task;
r = MSK_makeenv(&env, NULL);
if (r == MSK_RES_OK)
r = MSK_makeemptytask(env, &task);
if (r == MSK_RES_OK)
MSK_linkfunctotaskstream(task, MSK_STREAM_LOG, NULL, printstr);
if (r == MSK_RES_OK)
r = MSK_readlpstring(task,feasrepair_lp); /* Read problem from string */
if (r == MSK_RES_OK)
r = MSK_putintparam(task, MSK_IPAR_LOG_FEAS_REPAIR, 3);
if (r == MSK_RES_OK)
{
/* Weights are NULL implying all weights are 1. */
r = MSK_primalrepair(task, NULL, NULL, NULL, NULL);
}
if (r == MSK_RES_OK)
{
double sum_viol;
r = MSK_getdouinf(task, MSK_DINF_PRIMAL_REPAIR_PENALTY_OBJ, &sum_viol);
if (r == MSK_RES_OK)
{
printf("Minimized sum of violations = %e\n", sum_viol);
r = MSK_optimizetrm(task, &trmcode); /* Optimize the repaired task. */
MSK_solutionsummary(task, MSK_STREAM_MSG);
}
}
printf("Return code: %d\n", r);
return (r);
}
gp1.c
//
// Copyright: Copyright (c) MOSEK ApS, Denmark. All rights reserved.
//
// File: gp1.c
//
// Purpose: Demonstrates how to solve a simple Geometric Program (GP)
// cast into conic form with exponential cones and log-sum-exp.
//
// Example from
// https://gpkit.readthedocs.io/en/latest/examples.html//maximizing-the-volume-of-a-box
//
#include <stdio.h>
#include <math.h>
#include "mosek.h"
/* This function prints log output from MOSEK to the terminal. */
static void MSKAPI printstr(void *handle,
const char str[])
{
printf("%s", str);
} /* printstr */
// maximize h*w*d
// subjecto to 2*(h*w + h*d) <= Awall
// w*d <= Afloor
// alpha <= h/w <= beta
// gamma <= d/w <= delta
//
// Variable substitutions: h = exp(x), w = exp(y), d = exp(z).
//
// maximize x+y+z
// subject log( exp(x+y+log(2/Awall)) + exp(x+z+log(2/Awall)) ) <= 0
// y+z <= log(Afloor)
// log( alpha ) <= x-y <= log( beta )
// log( gamma ) <= z-y <= log( delta )
int max_volume_box(double Aw, double Af,
double alpha, double beta, double gamma, double delta,
double hwd[])
{
// Basic dimensions of our problem
const int numvar = 3; // Variables in original problem
const int numcon = 3; // Linear constraints in original problem
// Linear part of the problem involving x, y, z
const double cval[] = {1, 1, 1};
const int asubi[] = {0, 0, 1, 1, 2, 2};
const int asubj[] = {1, 2, 0, 1, 2, 1};
const int alen = 6;
const double aval[] = {1.0, 1.0, 1.0, -1.0, 1.0, -1.0};
const MSKboundkeye bkc[] = {MSK_BK_UP, MSK_BK_RA, MSK_BK_RA};
const double blc[] = {-MSK_INFINITY, log(alpha), log(gamma)};
const double buc[] = {log(Af), log(beta), log(delta)};
// Affine conic constraint data of the problem
MSKint64t expdomidx, rzerodomidx;
const MSKint64t numafe = 6, f_nnz = 8;
const MSKint64t afeidx[] = {0, 1, 2, 2, 3, 3, 5, 5};
const MSKint32t varidx[] = {3, 4, 0, 1, 0, 2, 3, 4};
const double f_val[] = {1, 1, 1, 1, 1, 1, 1, 1};
const double g[] = {0, 0, log(2/Aw), log(2/Aw), 1, -1};
MSKtask_t task = NULL;
MSKrescodee r = MSK_RES_OK, trmcode;
MSKsolstae solsta;
MSKint32t i;
double *xyz = (double*) calloc(numvar, sizeof(double));
if (r == MSK_RES_OK)
r = MSK_maketask(NULL, 0, 0, &task);
if (r == MSK_RES_OK)
r = MSK_linkfunctotaskstream(task, MSK_STREAM_LOG, NULL, printstr);
if (r == MSK_RES_OK)
r = MSK_appendvars(task, numvar);
if (r == MSK_RES_OK)
r = MSK_appendcons(task, numcon);
if (r == MSK_RES_OK)
r = MSK_appendafes(task, numafe);
// Objective is the sum of three first variables
if (r == MSK_RES_OK)
r = MSK_putobjsense(task, MSK_OBJECTIVE_SENSE_MAXIMIZE);
if (r == MSK_RES_OK)
r = MSK_putcslice(task, 0, numvar, cval);
if (r == MSK_RES_OK)
r = MSK_putvarboundsliceconst(task, 0, numvar, MSK_BK_FR, -MSK_INFINITY, +MSK_INFINITY);
// Add the three linear constraints
if (r == MSK_RES_OK)
r = MSK_putaijlist(task, alen, asubi, asubj, aval);
if (r == MSK_RES_OK)
r = MSK_putconboundslice(task, 0, numvar, bkc, blc, buc);
if (r == MSK_RES_OK)
{
MSKint64t acc1_afeidx[] = {0, 4, 2};
MSKint64t acc2_afeidx[] = {1, 4, 3};
MSKint64t acc3_afeidx[] = {5};
// Affine expressions appearing in affine conic constraints
// in this order:
// u1, u2, x+y+log(2/Awall), x+z+log(2/Awall), 1.0, u1+u2-1.0
if (r == MSK_RES_OK)
r = MSK_appendvars(task, 2);
if (r == MSK_RES_OK)
r = MSK_putvarboundsliceconst(task, numvar, numvar+2, MSK_BK_FR, -MSK_INFINITY, +MSK_INFINITY);
if (r == MSK_RES_OK)
r = MSK_putafefentrylist(task, f_nnz, afeidx, varidx, f_val);
if (r == MSK_RES_OK)
r = MSK_putafegslice(task, 0, numafe, g);
/* Append the primal exponential cone domain */
if (r == MSK_RES_OK)
r = MSK_appendprimalexpconedomain(task, &expdomidx);
/* (u1, 1, x+y+log(2/Awall)) \in EXP */
if (r == MSK_RES_OK)
r = MSK_appendacc(task, expdomidx, 3, acc1_afeidx, NULL);
/* (u2, 1, x+z+log(2/Awall)) \in EXP */
if (r == MSK_RES_OK)
r = MSK_appendacc(task, expdomidx, 3, acc2_afeidx, NULL);
/* The constraint u1+u2-1 \in \ZERO is added also as an ACC */
if (r == MSK_RES_OK)
r = MSK_appendrzerodomain(task, 1, &rzerodomidx);
if (r == MSK_RES_OK)
r = MSK_appendacc(task, rzerodomidx, 1, acc3_afeidx, NULL);
}
// Solve and map to original h, w, d
if (r == MSK_RES_OK)
r = MSK_optimizetrm(task, &trmcode);
if (r == MSK_RES_OK)
MSK_getsolsta(task, MSK_SOL_ITR, &solsta);
if (solsta == MSK_SOL_STA_OPTIMAL)
{
if (r == MSK_RES_OK)
r = MSK_getxxslice(task, MSK_SOL_ITR, 0, numvar, xyz);
for(i = 0; i < numvar; i++) hwd[i] = exp(xyz[i]);
}
else
{
printf("Solution not optimal, termination code %d.\n", trmcode);
r = trmcode;
}
free(xyz);
return r;
}
int main()
{
const double Aw = 200.0;
const double Af = 50.0;
const double alpha = 2.0;
const double beta = 10.0;
const double gamma = 2.0;
const double delta = 10.0;
MSKrescodee r;
double hwd[3];
r = max_volume_box(Aw, Af, alpha, beta, gamma, delta, hwd);
printf("Response code: %d\n", r);
if (r == MSK_RES_OK)
printf("Solution h=%.4f w=%.4f d=%.4f\n", hwd[0], hwd[1], hwd[2]);
return r;
}
helloworld.c
////
// Copyright: Copyright (c) MOSEK ApS, Denmark. All rights reserved.
//
// File: helloworld.c
//
// The most basic example of how to get started with MOSEK.
#include "mosek.h"
#include <stdio.h>
/* Error checking not included */
int main() {
MSKrescodee r, trmcode;
MSKenv_t env = NULL;
MSKtask_t task = NULL;
double xx = 0.0;
MSK_maketask(NULL, 0, 1, &task); // Create task
MSK_appendvars(task, 1); // 1 variable x
MSK_putcj(task, 0, 1.0); // c_0 = 1.0
MSK_putvarbound(task, 0, MSK_BK_RA, 2.0, 3.0); // 2.0 <= x <= 3.0
MSK_putobjsense(task, MSK_OBJECTIVE_SENSE_MINIMIZE); // Minimize
MSK_optimizetrm(task, &trmcode); // Optimize
MSK_getxx(task, MSK_SOL_ITR, &xx); // Get solution
printf("Solution x = %f\n", xx); // Print solution
MSK_deletetask(&task); // Clean up task
return 0;
}
lo1.c
/*
Copyright: Copyright (c) MOSEK ApS, Denmark. All rights reserved.
File: lo1.c
Purpose: To demonstrate how to solve a small linear
optimization problem using the MOSEK C API,
and handle the solver result and the problem
solution.
*/
#include <stdio.h>
#include "mosek.h"
/* This function prints log output from MOSEK to the terminal. */
static void MSKAPI printstr(void *handle,
const char str[])
{
printf("%s", str);
} /* printstr */
int main(int argc, const char *argv[])
{
const MSKint32t numvar = 4,
numcon = 3;
const double c[] = {3.0, 1.0, 5.0, 1.0};
/* Below is the sparse representation of the A
matrix stored by column. */
const MSKint32t aptrb[] = {0, 2, 5, 7},
aptre[] = {2, 5, 7, 9},
asub[] = { 0, 1,
0, 1, 2,
0, 1,
1, 2
};
const double aval[] = { 3.0, 2.0,
1.0, 1.0, 2.0,
2.0, 3.0,
1.0, 3.0
};
/* Bounds on constraints. */
const MSKboundkeye bkc[] = {MSK_BK_FX, MSK_BK_LO, MSK_BK_UP };
const double blc[] = {30.0, 15.0, -MSK_INFINITY};
const double buc[] = {30.0, +MSK_INFINITY, 25.0 };
/* Bounds on variables. */
const MSKboundkeye bkx[] = {MSK_BK_LO, MSK_BK_RA, MSK_BK_LO, MSK_BK_LO };
const double blx[] = {0.0, 0.0, 0.0, 0.0 };
const double bux[] = { +MSK_INFINITY, 10.0, +MSK_INFINITY, +MSK_INFINITY };
MSKtask_t task = NULL;
MSKrescodee r = MSK_RES_OK;
MSKint32t i, j;
if (r == MSK_RES_OK)
{
/* Create the optimization task. */
r = MSK_maketask(NULL, numcon, numvar, &task);
/* Directs the log task stream to the 'printstr' function. */
if (r == MSK_RES_OK)
r = MSK_linkfunctotaskstream(task, MSK_STREAM_LOG, NULL, printstr);
/* Append 'numcon' empty constraints.
The constraints will initially have no bounds. */
if (r == MSK_RES_OK)
r = MSK_appendcons(task, numcon);
/* Append 'numvar' variables.
The variables will initially be fixed at zero (x=0). */
if (r == MSK_RES_OK)
r = MSK_appendvars(task, numvar);
for (j = 0; j < numvar && r == MSK_RES_OK; ++j)
{
/* Set the linear term c_j in the objective.*/
if (r == MSK_RES_OK)
r = MSK_putcj(task, j, c[j]);
/* Set the bounds on variable j.
blx[j] <= x_j <= bux[j] */
if (r == MSK_RES_OK)
r = MSK_putvarbound(task,
j, /* Index of variable.*/
bkx[j], /* Bound key.*/
blx[j], /* Numerical value of lower bound.*/
bux[j]); /* Numerical value of upper bound.*/
/* Input column j of A */
if (r == MSK_RES_OK)
r = MSK_putacol(task,
j, /* Variable (column) index.*/
aptre[j] - aptrb[j], /* Number of non-zeros in column j.*/
asub + aptrb[j], /* Pointer to row indexes of column j.*/
aval + aptrb[j]); /* Pointer to Values of column j.*/
}
/* Set the bounds on constraints.
for i=1, ...,numcon : blc[i] <= constraint i <= buc[i] */
for (i = 0; i < numcon && r == MSK_RES_OK; ++i)
r = MSK_putconbound(task,
i, /* Index of constraint.*/
bkc[i], /* Bound key.*/
blc[i], /* Numerical value of lower bound.*/
buc[i]); /* Numerical value of upper bound.*/
/* Maximize objective function. */
if (r == MSK_RES_OK)
r = MSK_putobjsense(task, MSK_OBJECTIVE_SENSE_MAXIMIZE);
if (r == MSK_RES_OK)
{
MSKrescodee trmcode;
/* Run optimizer */
r = MSK_optimizetrm(task, &trmcode);
/* Print a summary containing information
about the solution for debugging purposes. */
MSK_solutionsummary(task, MSK_STREAM_LOG);
if (r == MSK_RES_OK)
{
MSKsolstae solsta;
if (r == MSK_RES_OK)
r = MSK_getsolsta(task,
MSK_SOL_BAS,
&solsta);
switch (solsta)
{
case MSK_SOL_STA_OPTIMAL:
{
double *xx = (double*) calloc(numvar, sizeof(double));
if (xx)
{
MSK_getxx(task,
MSK_SOL_BAS, /* Request the basic solution. */
xx);
printf("Optimal primal solution\n");
for (j = 0; j < numvar; ++j)
printf("x[%d]: %e\n", j, xx[j]);
free(xx);
}
else
r = MSK_RES_ERR_SPACE;
break;
}
case MSK_SOL_STA_DUAL_INFEAS_CER:
case MSK_SOL_STA_PRIM_INFEAS_CER:
printf("Primal or dual infeasibility certificate found.\n");
break;
case MSK_SOL_STA_UNKNOWN:
{
char symname[MSK_MAX_STR_LEN];
char desc[MSK_MAX_STR_LEN];
/* If the solutions status is unknown, print the termination code
indicating why the optimizer terminated prematurely. */
MSK_getcodedesc(trmcode,
symname,
desc);
printf("The solution status is unknown.\n");
printf("The optimizer terminitated with code: %s\n", symname);
break;
}
default:
printf("Other solution status.\n");
break;
}
}
}
if (r != MSK_RES_OK)
{
/* In case of an error print error code and description. */
char symname[MSK_MAX_STR_LEN];
char desc[MSK_MAX_STR_LEN];
printf("An error occurred while optimizing.\n");
MSK_getcodedesc(r,
symname,
desc);
printf("Error %s - '%s'\n", symname, desc);
}
/* Delete the task and the associated data. */
MSK_deletetask(&task);
}
return r;
}
lo2.c
/*
Copyright: Copyright (c) MOSEK ApS, Denmark. All rights reserved.
File: lo2.c
Purpose: To demonstrate how to solve a small linear
optimization problem using the MOSEK C API,
and handle the solver result and the problem
solution.
*/
#include <stdio.h>
#include "mosek.h"
/* This function prints log output from MOSEK to the terminal. */
static void MSKAPI printstr(void *handle,
const char str[])
{
printf("%s", str);
} /* printstr */
int main(int argc, const char *argv[])
{
const int numvar = 4,
numcon = 3;
double c[] = {3.0, 1.0, 5.0, 1.0};
/* Below is the sparse representation of the A
matrix stored by row. */
MSKint32t aptrb[] = {0, 3, 7};
MSKint32t aptre[] = {3, 7, 9};
MSKint32t asub[] = { 0, 1, 2,
0, 1, 2, 3,
1, 3
};
double aval[] = { 3.0, 1.0, 2.0,
2.0, 1.0, 3.0, 1.0,
2.0, 3.0
};
/* Bounds on constraints. */
MSKboundkeye bkc[] = {MSK_BK_FX, MSK_BK_LO, MSK_BK_UP };
double blc[] = {30.0, 15.0, -MSK_INFINITY};
double buc[] = {30.0, +MSK_INFINITY, 25.0 };
/* Bounds on variables. */
MSKboundkeye bkx[] = {MSK_BK_LO, MSK_BK_RA, MSK_BK_LO, MSK_BK_LO };
double blx[] = {0.0, 0.0, 0.0, 0.0 };
double bux[] = { +MSK_INFINITY, 10.0, +MSK_INFINITY, +MSK_INFINITY };
MSKenv_t env = NULL;
MSKtask_t task = NULL;
MSKrescodee r;
MSKint32t i, j;
/* Create the mosek environment. */
r = MSK_makeenv(&env, NULL);
if (r == MSK_RES_OK)
{
/* Create the optimization task. */
r = MSK_maketask(env, numcon, numvar, &task);
/* Directs the log task stream to the 'printstr' function. */
if (r == MSK_RES_OK)
r = MSK_linkfunctotaskstream(task, MSK_STREAM_LOG, NULL, printstr);
/* Append 'numcon' empty constraints.
The constraints will initially have no bounds. */
if (r == MSK_RES_OK)
r = MSK_appendcons(task, numcon);
/* Append 'numvar' variables.
The variables will initially be fixed at zero (x=0). */
if (r == MSK_RES_OK)
r = MSK_appendvars(task, numvar);
for (j = 0; j < numvar && r == MSK_RES_OK; ++j)
{
/* Set the linear term c_j in the objective.*/
if (r == MSK_RES_OK)
r = MSK_putcj(task, j, c[j]);
/* Set the bounds on variable j.
blx[j] <= x_j <= bux[j] */
if (r == MSK_RES_OK)
r = MSK_putvarbound(task,
j, /* Index of variable.*/
bkx[j], /* Bound key.*/
blx[j], /* Numerical value of lower bound.*/
bux[j]); /* Numerical value of upper bound.*/
}
/* Set the bounds on constraints.
for i=1, ...,numcon : blc[i] <= constraint i <= buc[i] */
for (i = 0; i < numcon && r == MSK_RES_OK; ++i)
{
r = MSK_putconbound(task,
i, /* Index of constraint.*/
bkc[i], /* Bound key.*/
blc[i], /* Numerical value of lower bound.*/
buc[i]); /* Numerical value of upper bound.*/
/* Input row i of A */
if (r == MSK_RES_OK)
r = MSK_putarow(task,
i, /* Row index.*/
aptre[i] - aptrb[i], /* Number of non-zeros in row i.*/
asub + aptrb[i], /* Pointer to column indexes of row i.*/
aval + aptrb[i]); /* Pointer to values of row i.*/
}
/* Maximize objective function. */
if (r == MSK_RES_OK)
r = MSK_putobjsense(task, MSK_OBJECTIVE_SENSE_MAXIMIZE);
if (r == MSK_RES_OK)
{
MSKrescodee trmcode;
/* Run optimizer */
r = MSK_optimizetrm(task, &trmcode);
/* Print a summary containing information
about the solution for debugging purposes. */
MSK_solutionsummary(task, MSK_STREAM_LOG);
if (r == MSK_RES_OK)
{
MSKsolstae solsta;
if (r == MSK_RES_OK)
r = MSK_getsolsta(task, MSK_SOL_BAS, &solsta);
switch (solsta)
{
case MSK_SOL_STA_OPTIMAL:
{
double *xx = (double*) calloc(numvar, sizeof(double));
if (xx)
{
MSK_getxx(task,
MSK_SOL_BAS, /* Request the basic solution. */
xx);
printf("Optimal primal solution\n");
for (j = 0; j < numvar; ++j)
printf("x[%d]: %e\n", j, xx[j]);
}
else
{
r = MSK_RES_ERR_SPACE;
}
free(xx);
break;
}
case MSK_SOL_STA_DUAL_INFEAS_CER:
case MSK_SOL_STA_PRIM_INFEAS_CER:
printf("Primal or dual infeasibility certificate found.\n");
break;
case MSK_SOL_STA_UNKNOWN:
{
char symname[MSK_MAX_STR_LEN];
char desc[MSK_MAX_STR_LEN];
/* If the solutions status is unknown, print the termination code
indicating why the optimizer terminated prematurely. */
MSK_getcodedesc(trmcode,
symname,
desc);
printf("The solutuion status is unknown.\n");
printf("The optimizer terminitated with code: %s\n", symname);
break;
}
default:
printf("Other solution status.\n");
break;
}
}
}
if (r != MSK_RES_OK)
{
/* In case of an error print error code and description. */
char symname[MSK_MAX_STR_LEN];
char desc[MSK_MAX_STR_LEN];
printf("An error occurred while optimizing.\n");
MSK_getcodedesc(r,
symname,
desc);
printf("Error %s - '%s'\n", symname, desc);
}
/* Delete the task and the associated data. */
MSK_deletetask(&task);
}
/* Delete the environment and the associated data. */
MSK_deleteenv(&env);
return r;
}
logistic.c
////
// Copyright: Copyright (c) MOSEK ApS, Denmark. All rights reserved.
//
// File: logistic.c
//
// Purpose: Implements logistic regression with regulatization.
//
// Demonstrates using the exponential cone and log-sum-exp in Optimizer API.
#include <stdio.h>
#include "mosek.h" /* Include the MOSEK definition file. */
#define MSKCALL(x) if (res==MSK_RES_OK) res = (x);
static void MSKAPI printstr(void *handle,
const char str[])
{
printf("%s", str);
} /* printstr */
const double inf = 0.0;
// Adds ACCs for t_i >= log ( 1 + exp((1-2*y[i]) * theta' * X[i]) )
// Adds auxiliary variables, AFE rows and constraints
MSKrescodee softplus(MSKtask_t task, int d, int n, MSKint32t theta, MSKint32t t, double* X, int* y)
{
MSKint32t nvar, ncon;
MSKint64t nafe, thetaafe, tafe, z1afe, z2afe, oneafe, expdomain;
MSKint32t z1, z2, zcon, v1con, v2con;
MSKint32t *subi = (MSKint32t*) calloc(2*n, sizeof(MSKint32t));
MSKint32t *subj = (MSKint32t*) calloc(3*n, sizeof(MSKint32t));
MSKrealt *aval = (MSKrealt*) calloc(2*n, sizeof(MSKrealt));
MSKint64t *afeidx = (MSKint64t*) calloc(d*n+4*n, sizeof(MSKint64t));
MSKint32t *varidx = (MSKint32t*) calloc(d*n+4*n, sizeof(MSKint32t));
MSKrealt *fval = (MSKrealt*) calloc(d*n+4*n, sizeof(MSKrealt));
MSKint64t idx[3];
int k, i, j;
MSKrescodee res = MSK_RES_OK;
MSKCALL(MSK_getnumvar(task, &nvar));
MSKCALL(MSK_getnumcon(task, &ncon));
MSKCALL(MSK_getnumafe(task, &nafe));
MSKCALL(MSK_appendvars(task, 2*n)); // z1, z2
MSKCALL(MSK_appendcons(task, n)); // z1 + z2 = 1
MSKCALL(MSK_appendafes(task, 4*n)); //theta * X[i] - t[i], -t[i], z1[i], z2[i]
z1 = nvar, z2 = nvar+n;
zcon = ncon;
thetaafe = nafe, tafe = nafe+n, z1afe = nafe+2*n, z2afe = nafe+3*n;
// Linear constraints
k = 0;
for(i = 0; i < n; i++)
{
// z1 + z2 = 1
subi[k] = zcon+i; subj[k] = z1+i; aval[k] = 1; k++;
subi[k] = zcon+i; subj[k] = z2+i; aval[k] = 1; k++;
}
MSKCALL(MSK_putaijlist(task, 2*n, subi, subj, aval));
MSKCALL(MSK_putconboundsliceconst(task, zcon, zcon+n, MSK_BK_FX, 1, 1));
MSKCALL(MSK_putvarboundsliceconst(task, nvar, nvar+2*n, MSK_BK_FR, -inf, inf));
// Affine conic expressions
k = 0;
// Thetas
for(i = 0; i < n; i++) {
for(j = 0; j < d; j++) {
afeidx[k] = thetaafe + i; varidx[k] = theta + j;
fval[k] = ((y[i]) ? -1 : 1) * X[i*d+j];
k++;
}
}
// -t[i]
for(i = 0; i < n; i++) {
afeidx[k] = thetaafe + i; varidx[k] = t + i; fval[k] = -1; k++;
afeidx[k] = tafe + i; varidx[k] = t + i; fval[k] = -1; k++;
}
// z1, z2
for(i = 0; i < n; i++) {
afeidx[k] = z1afe + i; varidx[k] = z1 + i; fval[k] = 1; k++;
afeidx[k] = z2afe + i; varidx[k] = z2 + i; fval[k] = 1; k++;
}
// Add the expressions
MSKCALL(MSK_putafefentrylist(task, d*n+4*n, afeidx, varidx, fval));
// Add a single row with the constant expression "1.0"
MSKCALL(MSK_getnumafe(task, &oneafe));
MSKCALL(MSK_appendafes(task,1));
MSKCALL(MSK_putafeg(task, oneafe, 1.0));
// Add an exponential cone domain
MSKCALL(MSK_appendprimalexpconedomain(task, &expdomain));
// Conic constraints
for(i = 0; i < n; i++)
{
idx[0] = z1afe+i, idx[1] = oneafe, idx[2] = thetaafe+i;
MSKCALL(MSK_appendacc(task, expdomain, 3, idx, NULL));
idx[0] = z2afe+i, idx[1] = oneafe, idx[2] = tafe+i;
MSKCALL(MSK_appendacc(task, expdomain, 3, idx, NULL));
}
free(subi); free(subj); free(aval);
free(afeidx); free(varidx); free(fval);
return res;
}
// Model logistic regression (regularized with full 2-norm of theta)
// X - n x d matrix of data points
// y - length n vector classifying training points
// lamb - regularization parameter
MSKrescodee logisticRegression(MSKenv_t env,
int n, // num samples
int d, // dimension
double *X,
int *y,
double lamb,
double *thetaVal) // result
{
MSKrescodee res = MSK_RES_OK;
MSKrescodee trm = MSK_RES_OK;
MSKtask_t task = NULL;
MSKint32t nvar = 1+d+n;
MSKint32t r = 0, theta = 1, t = 1+d;
MSKint64t numafe, quadDom;
int i = 0;
MSKCALL(MSK_maketask(env, 0, 0, &task));
MSKCALL(MSK_linkfunctotaskstream(task, MSK_STREAM_LOG, NULL, printstr));
// Variables [r; theta; t]
MSKCALL(MSK_appendvars(task, nvar));
MSKCALL(MSK_putvarboundsliceconst(task, 0, nvar, MSK_BK_FR, -inf, inf));
// Objective lambda*r + sum(t)
MSKCALL(MSK_putobjsense(task, MSK_OBJECTIVE_SENSE_MINIMIZE));
MSKCALL(MSK_putcj(task, r, lamb));
for(i = 0; i < n && res == MSK_RES_OK; i++)
MSKCALL(MSK_putcj(task, t+i, 1.0));
// Softplus function constraints
MSKCALL(softplus(task, d, n, theta, t, X, y));
// Regularization
// Append a sequence of linear expressions (r, theta) to F
MSKCALL(MSK_getnumafe(task, &numafe));
MSKCALL(MSK_appendafes(task,1+d));
MSKCALL(MSK_putafefentry(task, numafe, r, 1.0));
for(i = 0; i < d; i++)
MSKCALL(MSK_putafefentry(task, numafe + i + 1, theta + i, 1.0));
// Add the constraint
MSKCALL(MSK_appendquadraticconedomain(task, 1+d, &quadDom));
MSKCALL(MSK_appendaccseq(task, quadDom, 1+d, numafe, NULL));
// Solution
MSKCALL(MSK_optimizetrm(task, &trm));
MSKCALL(MSK_solutionsummary(task, MSK_STREAM_MSG));
MSKCALL(MSK_getxxslice(task, MSK_SOL_ITR, theta, theta+d, thetaVal));
return res;
}
int main()
{
MSKenv_t env;
MSKrescodee res = MSK_RES_OK;
MSKCALL(MSK_makeenv(&env, NULL));
// Test: detect and approximate a circle using degree 2 polynomials
{
int n = 30;
double X[6*30*30];
int Y[30*30];
int i,j;
double theta[6];
for(i=0; i<n; i++)
for(j=0; j<n; j++)
{
int k = i*n+j;
double x = -1 + 2.0*i/(n-1);
double y = -1 + 2.0*j/(n-1);
X[6*k+0] = 1.0; X[6*k+1] = x; X[6*k+2] = y; X[6*k+3] = x*y;
X[6*k+4] = x*x; X[6*k+5] = y*y;
Y[k] = (x*x+y*y>=0.69) ? 1 : 0;
}
MSKCALL(logisticRegression(env, n*n, 6, X, Y, 0.1, theta));
if (res == MSK_RES_OK)
for(i=0;i<6;i++) printf("%.4f\n", theta[i]);
}
return res;
}
mico1.c
/*
Copyright : Copyright (c) MOSEK ApS, Denmark. All rights reserved.
File : mico1.c
Purpose : Demonstrates how to solve a small mixed
integer conic optimization problem.
minimize x^2 + y^2
subject to x >= e^y + 3.8
x, y - integer
*/
#include <stdio.h>
#include "mosek.h" /* Include the MOSEK definition file. */
static void MSKAPI printstr(void *handle,
const char str[])
{
printf("%s", str);
} /* printstr */
int main(int argc, char *argv[])
{
MSKint32t numvar = 3; /* x, y, t */
MSKvariabletypee vart[] = { MSK_VAR_TYPE_INT, MSK_VAR_TYPE_INT };
MSKint32t intsub[] = { 0, 1 };
MSKint32t i, j;
MSKenv_t env = NULL;
MSKtask_t task = NULL;
MSKrescodee r, trm;
r = MSK_makeenv(&env, NULL);
if (r == MSK_RES_OK)
{
r = MSK_maketask(env, 0, 0, &task);
if (r == MSK_RES_OK)
r = MSK_linkfunctotaskstream(task, MSK_STREAM_LOG, NULL, printstr);
if (r == MSK_RES_OK)
r = MSK_appendvars(task, numvar);
if (r == MSK_RES_OK)
r = MSK_putvarboundsliceconst(task, 0, numvar, MSK_BK_FR, -0.0, 0.0);
/* Integrality constraints */
if (r == MSK_RES_OK)
r = MSK_putvartypelist(task, 2, intsub, vart);
/* Objective */
if (r == MSK_RES_OK)
r = MSK_putobjsense(task, MSK_OBJECTIVE_SENSE_MINIMIZE);
if (r == MSK_RES_OK)
r = MSK_putcj(task, 2, 1.0); /* Minimize t */
/* Conic part of the problem */
if (r == MSK_RES_OK)
{
/* Set up the affine expressions */
/* x, x-3.8, y, t, 1.0 */
MSKint64t afeidx[] = {0, 1, 2, 3};
MSKint32t varidx[] = {0, 0, 1, 2};
MSKrealt val[] = {1.0, 1.0, 1.0, 1.0};
MSKrealt g[] = {0.0, -3.8, 0.0, 0.0, 1.0};
MSKint64t domExp, domQuad;
MSKint64t afeidxExp[] = {1, 4, 2};
MSKint64t afeidxQuad[] = {3, 0, 2};
if (r == MSK_RES_OK)
r = MSK_appendafes(task, 5);
if (r == MSK_RES_OK)
r = MSK_putafefentrylist(task,
4,
afeidx,
varidx,
val);
if (r == MSK_RES_OK)
r = MSK_putafegslice(task, 0, 5, g);
// Add constraint (x-3.8, 1, y) \in \EXP
if (r == MSK_RES_OK)
r = MSK_appendprimalexpconedomain(task, &domExp);
if (r == MSK_RES_OK)
r = MSK_appendacc(task, domExp, 3, afeidxExp, NULL);
// Add constraint (t, x, y) \in \QUAD
if (r == MSK_RES_OK)
r = MSK_appendquadraticconedomain(task, 3, &domQuad);
if (r == MSK_RES_OK)
r = MSK_appendacc(task, domQuad, 3, afeidxQuad, NULL);
}
/* Optimize the problem */
if (r == MSK_RES_OK)
r = MSK_optimizetrm(task, &trm);
if (r == MSK_RES_OK)
r = MSK_solutionsummary(task, MSK_STREAM_MSG);
if (r == MSK_RES_OK)
{
MSKrealt xx[] = {0, 0};
r = MSK_getxxslice(task, MSK_SOL_ITG, 0, 2, xx);
if (r == MSK_RES_OK)
printf("x = %.2f, y = %.2f\n", xx[0], xx[1]);
}
if (task) MSK_deletetask(&task);
}
if (env) MSK_deleteenv(&env);
return r;
}
milo1.c
/*
Copyright: Copyright (c) MOSEK ApS, Denmark. All rights reserved.
File: milo1.c
Purpose: To demonstrate how to solve a small mixed
integer linear optimization problem using
the MOSEK API.
*/
#include <stdio.h>
#include "mosek.h" /* Include the MOSEK definition file. */
static void MSKAPI printstr(void *handle,
const char str[])
{
printf("%s", str);
} /* printstr */
int main(int argc, char *argv[])
{
const MSKint32t numvar = 2,
numcon = 2;
double c[] = { 1.0, 0.64 };
MSKboundkeye bkc[] = { MSK_BK_UP, MSK_BK_LO };
double blc[] = { -MSK_INFINITY, -4.0 };
double buc[] = { 250.0, MSK_INFINITY };
MSKboundkeye bkx[] = { MSK_BK_LO, MSK_BK_LO };
double blx[] = { 0.0, 0.0 };
double bux[] = { MSK_INFINITY, MSK_INFINITY };
MSKint32t aptrb[] = { 0, 2 },
aptre[] = { 2, 4 },
asub[] = { 0, 1, 0, 1 };
double aval[] = { 50.0, 3.0, 31.0, -2.0 };
MSKint32t i, j;
MSKenv_t env = NULL;
MSKtask_t task = NULL;
MSKrescodee r;
/* Create the mosek environment. */
r = MSK_makeenv(&env, NULL);
/* Check if return code is ok. */
if (r == MSK_RES_OK)
{
/* Create the optimization task. */
r = MSK_maketask(env, 0, 0, &task);
if (r == MSK_RES_OK)
r = MSK_linkfunctotaskstream(task, MSK_STREAM_LOG, NULL, printstr);
/* Append 'numcon' empty constraints.
The constraints will initially have no bounds. */
if (r == MSK_RES_OK)
r = MSK_appendcons(task, numcon);
/* Append 'numvar' variables.
The variables will initially be fixed at zero (x=0). */
if (r == MSK_RES_OK)
r = MSK_appendvars(task, numvar);
/* Optionally add a constant term to the objective. */
if (r == MSK_RES_OK)
r = MSK_putcfix(task, 0.0);
for (j = 0; j < numvar && r == MSK_RES_OK; ++j)
{
/* Set the linear term c_j in the objective.*/
if (r == MSK_RES_OK)
r = MSK_putcj(task, j, c[j]);
/* Set the bounds on variable j.
blx[j] <= x_j <= bux[j] */
if (r == MSK_RES_OK)
r = MSK_putvarbound(task,
j, /* Index of variable.*/
bkx[j], /* Bound key.*/
blx[j], /* Numerical value of lower bound.*/
bux[j]); /* Numerical value of upper bound.*/
/* Input column j of A */
if (r == MSK_RES_OK)
r = MSK_putacol(task,
j, /* Variable (column) index.*/
aptre[j] - aptrb[j], /* Number of non-zeros in column j.*/
asub + aptrb[j], /* Pointer to row indexes of column j.*/
aval + aptrb[j]); /* Pointer to Values of column j.*/
}
/* Set the bounds on constraints.
for i=1, ...,numcon : blc[i] <= constraint i <= buc[i] */
for (i = 0; i < numcon && r == MSK_RES_OK; ++i)
r = MSK_putconbound(task,
i, /* Index of constraint.*/
bkc[i], /* Bound key.*/
blc[i], /* Numerical value of lower bound.*/
buc[i]); /* Numerical value of upper bound.*/
/* Specify integer variables. */
for (j = 0; j < numvar && r == MSK_RES_OK; ++j)
r = MSK_putvartype(task, j, MSK_VAR_TYPE_INT);
if (r == MSK_RES_OK)
r = MSK_putobjsense(task,
MSK_OBJECTIVE_SENSE_MAXIMIZE);
if (r == MSK_RES_OK)
/* Set max solution time */
r = MSK_putdouparam(task,
MSK_DPAR_MIO_MAX_TIME,
60.0);
if (r == MSK_RES_OK)
{
MSKrescodee trmcode;
/* Run optimizer */
r = MSK_optimizetrm(task, &trmcode);
/* Print a summary containing information
about the solution for debugging purposes*/
MSK_solutionsummary(task, MSK_STREAM_MSG);
if (r == MSK_RES_OK)
{
MSKint32t j;
MSKsolstae solsta;
double *xx = NULL;
MSK_getsolsta(task, MSK_SOL_ITG, &solsta);
xx = calloc(numvar, sizeof(double));
if (xx)
{
switch (solsta)
{
case MSK_SOL_STA_INTEGER_OPTIMAL:
MSK_getxx(task,
MSK_SOL_ITG, /* Request the integer solution. */
xx);
printf("Optimal solution.\n");
for (j = 0; j < numvar; ++j)
printf("x[%d]: %e\n", j, xx[j]);
break;
case MSK_SOL_STA_PRIM_FEAS:
/* A feasible but not necessarily optimal solution was located. */
MSK_getxx(task, MSK_SOL_ITG, xx);
printf("Feasible solution.\n");
for (j = 0; j < numvar; ++j)
printf("x[%d]: %e\n", j, xx[j]);
break;
case MSK_SOL_STA_UNKNOWN:
{
MSKprostae prosta;
MSK_getprosta(task, MSK_SOL_ITG, &prosta);
switch (prosta)
{
case MSK_PRO_STA_PRIM_INFEAS_OR_UNBOUNDED:
printf("Problem status Infeasible or unbounded\n");
break;
case MSK_PRO_STA_PRIM_INFEAS:
printf("Problem status Infeasible.\n");
break;
case MSK_PRO_STA_UNKNOWN:
printf("Problem status unknown. Termination code %d.\n", trmcode);
break;
default:
printf("Other problem status.");
break;
}
}
break;
default:
printf("Other solution status.");
break;
}
}
else
{
r = MSK_RES_ERR_SPACE;
}
free(xx);
}
}
if (r != MSK_RES_OK)
{
/* In case of an error print error code and description. */
char symname[MSK_MAX_STR_LEN];
char desc[MSK_MAX_STR_LEN];
printf("An error occurred while optimizing.\n");
MSK_getcodedesc(r,
symname,
desc);
printf("Error %s - '%s'\n", symname, desc);
}
MSK_deletetask(&task);
}
MSK_deleteenv(&env);
printf("Return code: %d.\n", r);
return (r);
} /* main */
mioinitsol.c
/*
Copyright: Copyright (c) MOSEK ApS, Denmark. All rights reserved.
File: mioinitsol.c
Purpose: To demonstrate how to solve a MIP with a start guess.
*/
#include "mosek.h"
#include <stdio.h>
static void MSKAPI printstr(void *handle,
const char str[])
{
printf("%s", str);
} /* printstr */
int main(int argc, char *argv[])
{
char buffer[512];
const MSKint32t numvar = 4,
numcon = 1,
numintvar = 3;
MSKrescodee r;
MSKenv_t env;
MSKtask_t task;
double c[] = { 7.0, 10.0, 1.0, 5.0 };
MSKboundkeye bkc[] = {MSK_BK_UP};
double blc[] = { -MSK_INFINITY};
double buc[] = {2.5};
MSKboundkeye bkx[] = {MSK_BK_LO, MSK_BK_LO, MSK_BK_LO, MSK_BK_LO};
double blx[] = {0.0, 0.0, 0.0, 0.0 };
double bux[] = {MSK_INFINITY, MSK_INFINITY, MSK_INFINITY, MSK_INFINITY};
MSKint32t ptrb[] = {0, 1, 2, 3},
ptre[] = {1, 2, 3, 4},
asub[] = {0, 0, 0, 0 };
double aval[] = {1.0, 1.0, 1.0, 1.0};
MSKint32t intsub[] = {0, 1, 2};
MSKint32t j;
double xx[4];
r = MSK_makeenv(&env, NULL);
if (r == MSK_RES_OK)
r = MSK_maketask(env, 0, 0, &task);
if (r == MSK_RES_OK)
r = MSK_linkfunctotaskstream(task, MSK_STREAM_LOG, NULL, printstr);
if (r == MSK_RES_OK)
r = MSK_inputdata(task,
numcon, numvar,
numcon, numvar,
c,
0.0,
ptrb,
ptre,
asub,
aval,
bkc,
blc,
buc,
bkx,
blx,
bux);
if (r == MSK_RES_OK)
r = MSK_putobjsense(task, MSK_OBJECTIVE_SENSE_MAXIMIZE);
for (j = 0; j < numintvar && r == MSK_RES_OK; ++j)
r = MSK_putvartype(task, intsub[j], MSK_VAR_TYPE_INT);
if (r == MSK_RES_OK)
{
/* Assign values to integer variables
(we only set a slice of xx) */
double xxInit[] = {1.0, 1.0, 0.0};
r = MSK_putxxslice(task, MSK_SOL_ITG, 0, 3, xxInit);
}
if (r == MSK_RES_OK)
{
/* Request constructing the solution from integer variable values */
r = MSK_putintparam(task, MSK_IPAR_MIO_CONSTRUCT_SOL, MSK_ON);
}
/* solve */
if (r == MSK_RES_OK)
{
MSKrescodee trmcode;
r = MSK_optimizetrm(task, &trmcode);
MSK_solutionsummary(task, MSK_STREAM_LOG);
}
/* Read back the solution */
r = MSK_getxx(task, MSK_SOL_ITG, xx);
if (r == MSK_RES_OK)
{
int constr;
double constr_obj;
printf("Solution:\n");
for(j = 0; j < numvar; j++)
printf("%f ", xx[j]);
printf("\n");
/* Was the initial guess used? */
MSK_getintinf(task, MSK_IINF_MIO_CONSTRUCT_SOLUTION, &constr);
MSK_getdouinf(task, MSK_DINF_MIO_CONSTRUCT_SOLUTION_OBJ, &constr_obj);
printf("Construct solution utilization: %d\nConstruct solution objective: %.3f\n", constr, constr_obj);
}
else
{
/* In case of an error print error code and description. */
char symname[MSK_MAX_STR_LEN];
char desc[MSK_MAX_STR_LEN];
printf("An error occurred while optimizing.\n");
MSK_getcodedesc(r,
symname,
desc);
printf("Error %s - '%s'\n", symname, desc);
}
MSK_deletetask(&task);
MSK_deleteenv(&env);
return (r);
}
opt_server_async.c
/*
Copyright: Copyright (c) MOSEK ApS, Denmark. All rights reserved.
File: opt_server_async.c
Purpose : Demonstrates how to use MOSEK OptServer
to solve optimization problem asynchronously
*/
#include "mosek.h"
#ifdef _WIN32
#include "windows.h"
#else
#include "unistd.h"
#endif
static void MSKAPI printstr(void *handle, const char str[])
{
printf("%s", str);
}
int main(int argc, char * argv[])
{
char token[33];
int numpolls = 10;
int i = 0;
MSKbooleant respavailable;
MSKenv_t env = NULL;
MSKtask_t task = NULL;
MSKrescodee res = MSK_RES_OK;
MSKrescodee trm;
MSKrescodee resp;
const char * filename = "../data/25fv47.mps";
const char * addr = "solve.mosek.com:30080";
const char * cert = NULL;
if (argc < 4)
{
fprintf(stderr, "Syntax: opt_server_async filename host:port numpolls [cert]\n");
return 0;
}
filename = argv[1];
addr = argv[2];
numpolls = atoi(argv[3]);
cert = argc < 5 ? NULL : argv[4];
res = MSK_makeenv(&env, NULL);
if (res == MSK_RES_OK)
res = MSK_maketask(env, 0, 0, &task);
if (res == MSK_RES_OK)
res = MSK_linkfunctotaskstream(task, MSK_STREAM_LOG, NULL, printstr);
if (res == MSK_RES_OK)
res = MSK_readdata(task, filename);
if (MSK_RES_OK == res && cert)
res = MSK_putstrparam(task, MSK_SPAR_REMOTE_TLS_CERT_PATH,cert);
res = MSK_asyncoptimize(task,
addr,
"",
token);
MSK_deletetask(&task);
printf("token = %s\n", token);
if (res == MSK_RES_OK)
res = MSK_maketask(env, 0, 0, &task);
if (res == MSK_RES_OK)
res = MSK_readdata(task, filename);
if (MSK_RES_OK == res && cert)
res = MSK_putstrparam(task, MSK_SPAR_REMOTE_TLS_CERT_PATH,cert);
if (res == MSK_RES_OK)
res = MSK_linkfunctotaskstream(task, MSK_STREAM_LOG, NULL, printstr);
for (i = 0; i < numpolls && res == MSK_RES_OK ; i++)
{
#if __linux__
sleep(1);
#elif defined(_WIN32)
Sleep(1000);
#endif
puts("+++++++++++++++++++++++++++++++++++++++++++++++++++++\n");
printf("poll %d\n ", i);
res = MSK_asyncpoll(task,
addr,
"",
token,
&respavailable,
&resp,
&trm);
puts("polling done\n");
puts("+++++++++++++++++++++++++++++++++++++++++++++++++++++\n");
if (respavailable)
{
puts("solution available!");
res = MSK_asyncgetresult(task,
addr,
"",
token,
&respavailable,
&resp,
&trm);
MSK_solutionsummary(task, MSK_STREAM_LOG);
break;
}
}
if (i == numpolls)
{
printf("max num polls reached, stopping %s", addr);
MSK_asyncstop(task, addr, "", token);
}
MSK_deletetask(&task);
MSK_deleteenv(&env);
printf("%s:%d: Result = %d\n", __FILE__, __LINE__, res); fflush(stdout);
return res;
}
opt_server_sync.c
/*
Copyright: Copyright (c) MOSEK ApS, Denmark. All rights reserved.
File: opt_server_sync.c
Purpose : Demonstrates how to use MOSEK OptServer
to solve optimization problem synchronously
*/
#include "mosek.h"
static void MSKAPI printstr(void *handle, const char str[])
{
printf("%s", str);
}
int main(int argc, const char * argv[])
{
MSKenv_t env = NULL;
MSKtask_t task = NULL;
MSKrescodee res = MSK_RES_OK;
MSKrescodee trm = MSK_RES_OK;
if (argc <= 3)
{
fprintf(stderr, "Syntax: opt_server_sync inputfile addr [certpath]\n");
return 0;
}
else
{
const char * taskfile = argv[1];
const char * address = argv[2];
const char * certfile = argc > 3 ? argv[3] : NULL;
// Create the mosek environment.
// The `NULL' arguments here, are used to specify customized
// memory allocators and a memory debug file. These can
// safely be ignored for now.
res = MSK_makeenv(&env, NULL);
// Create a task object linked with the environment env.
// We create it with 0 variables and 0 constraints initially,
// since we do not know the size of the problem.
if (res == MSK_RES_OK)
res = MSK_maketask(env, 0, 0, &task);
// Direct the task log stream to a user specified function
if (res == MSK_RES_OK)
res = MSK_linkfunctotaskstream(task, MSK_STREAM_LOG, NULL, printstr);
// We assume that a problem file was given as the first command
// line argument (received in `argv')
if (res == MSK_RES_OK)
res = MSK_readdata(task, taskfile);
// Set OptServer URL
if (res == MSK_RES_OK)
res = MSK_putoptserverhost(task, address);
// Path to certificate, if any
if (MSK_RES_OK == res && certfile)
res = MSK_putstrparam(task, MSK_SPAR_REMOTE_TLS_CERT_PATH,certfile);
// Solve the problem remotely
if (res == MSK_RES_OK)
res = MSK_optimizetrm(task, &trm);
// Print a summary of the solution.
if (res == MSK_RES_OK)
res = MSK_solutionsummary(task, MSK_STREAM_LOG);
// Delete task and environment
MSK_deletetask(&task);
MSK_deleteenv(&env);
}
return res;
}
parallel.c
/*
Copyright: Copyright (c) MOSEK ApS, Denmark. All rights reserved.
File: parallel.c
Purpose: Demonstrates parallel optimization usint optimizebatch()
*/
#include<stdio.h>
#include<stdlib.h>
#include<mosek.h>
/** Example of how to use MSK_optimizebatch().
Optimizes tasks whose names were read from command line.
*/
int main(int argc, char **argv)
{
MSKenv_t env;
int n = argc - 1;
MSKtask_t *tasks = NULL;
MSKrescodee *res = NULL;
MSKrescodee *trm = NULL;
MSKrescodee r = MSK_RES_OK;
int i;
/* Size of thread pool available for all tasks */
int threadpoolsize = 6;
tasks = calloc(n, sizeof(MSKtask_t));
res = calloc(n, sizeof(MSKrescodee));
trm = calloc(n, sizeof(MSKrescodee));
MSK_makeenv(&env, NULL);
/* Create an example list of tasks to optimize */
for (i = 0; i < n; i++) {
MSK_makeemptytask(env, &(tasks[i]));
MSK_readdata(tasks[i], argv[i+1]);
/* We can set the number of threads for each task */
MSK_putintparam(tasks[i], MSK_IPAR_NUM_THREADS, 2);
}
/* Optimize all the given tasks in parallel */
r = MSK_optimizebatch(env,
0, // No race
-1.0, // No time limit
threadpoolsize,
n,
tasks, // Array of tasks to optimize
trm,
res);
for(i = 0; i < n; i++) {
double obj, tm;
MSK_getdouinf(tasks[i], MSK_DINF_INTPNT_PRIMAL_OBJ, &obj);
MSK_getdouinf(tasks[i], MSK_DINF_OPTIMIZER_TIME, &tm);
printf("Task %d res %d trm %d obj_val %.5f time %.5f\n",
i,
res[i],
trm[i],
obj,
tm);
}
for(i = 0; i < n; i++)
MSK_deletetask(&(tasks[i]));
free(tasks);
free(trm);
free(res);
MSK_deleteenv(&env);
return 0;
}
parameters.c
/*
Copyright: Copyright (c) MOSEK ApS, Denmark. All rights reserved.
File: parameters.c
Purpose: Demonstrates a very simple example about how to get/set
parameters with MOSEK C API
*/
#include "mosek.h"
#include "stdio.h"
int main()
{
MSKenv_t env = NULL;
MSKtask_t task = NULL;
MSKrescodee res, trmcode;
double param = 0.0;
double tm;
MSKint32t iter;
/* Create an environment */
res = MSK_makeenv(&env, NULL);
if (res == MSK_RES_OK)
{
/* Create a task */
res = MSK_maketask(env, 0, 0, &task);
if (res == MSK_RES_OK)
{
printf("Test MOSEK parameter get/set functions\n");
// Set log level (integer parameter)
res = MSK_putintparam(task, MSK_IPAR_LOG, 1);
// Select interior-point optimizer... (integer parameter)
res = MSK_putintparam(task, MSK_IPAR_OPTIMIZER, MSK_OPTIMIZER_INTPNT);
// ... without basis identification (integer parameter)
res = MSK_putintparam(task, MSK_IPAR_INTPNT_BASIS, MSK_BI_NEVER);
// Set relative gap tolerance (double parameter)
res = MSK_putdouparam(task, MSK_DPAR_INTPNT_CO_TOL_REL_GAP, 1.0e-7);
// The same using explicit string names
res = MSK_putparam(task, "MSK_DPAR_INTPNT_CO_TOL_REL_GAP", "1.0e-7");
res = MSK_putnadouparam(task, "MSK_DPAR_INTPNT_CO_TOL_REL_GAP", 1.0e-7);
// Incorrect value
res = MSK_putdouparam(task, MSK_DPAR_INTPNT_CO_TOL_REL_GAP, -1.0);
if (res != MSK_RES_OK)
printf("Wrong parameter value\n");
res = MSK_getdouparam(task, MSK_DPAR_INTPNT_CO_TOL_REL_GAP, ¶m);
printf("Current value for parameter MSK_DPAR_INTPNT_CO_TOL_REL_GAP = %e\n", param);
/* Define and solve an optimization problem here */
/* MSK_optimizetrm(task, &trmcode) */
/* After optimization: */
printf("Get MOSEK information items\n");
res = MSK_getdouinf(task, MSK_DINF_OPTIMIZER_TIME, &tm);
res = MSK_getintinf(task, MSK_IINF_INTPNT_ITER, &iter);
printf("Time: %f\nIterations: %d\n", tm, iter);
MSK_deletetask(&task);
}
MSK_deleteenv(&env);
}
return 0;
}
pinfeas.c
// File : pinfeas.c
//
// Copyright : Copyright (c) MOSEK ApS, Denmark. All rights reserved.
//
// Purpose: Demonstrates how to fetch a primal infeasibility certificate
// for a linear problem
//
#include <stdio.h>
#include "mosek.h"
#include <math.h>
/* This function prints log output from MOSEK to the terminal. */
static void MSKAPI printstr(void *handle,
const char str[])
{
printf("%s", str);
} /* printstr */
// Set up a simple linear problem from the manual for test purposes
static MSKrescodee testProblem(MSKtask_t *task) {
MSKrescodee r = MSK_RES_OK;
const char data[] = "Task ''\n\
Objective ''\n\
Minimize + @x0 + 2 @x1 + 5 @x2 + 2 @x3 + @x4 + 2 @x5 + @x6\n\
Constraints\n\
@c0 [-inf;200] + @x0 + @x1\n\
@c1 [-inf;1000] + @x2 + @x3\n\
@c2 [-inf;1000] + @x4 + @x5 + @x6\n\
@c3 [1100] + @x0 + @x4\n\
@c4 [200] + @x1\n\
@c5 [500] + @x2 + @x5\n\
@c6 [500] + @x3 + @x6\n\
Variables\n\
@x0 [0;+inf]\n\
@x1 [0;+inf]\n\
@x2 [0;+inf]\n\
@x3 [0;+inf]\n\
@x4 [0;+inf]\n\
@x5 [0;+inf]\n\
@x6 [0;+inf]\n";
r = MSK_makeemptytask(NULL, task);
if (r == MSK_RES_OK)
r = MSK_readptfstring(*task, data);
return r;
}
// Analyzes and prints infeasibility contributing elements
// n - length of arrays
// sl - dual values for lower bounds
// su - dual values for upper bounds
// eps - tolerance for when a nunzero dual value is significant
static void analyzeCertificate(MSKint32t n, MSKrealt *sl, MSKrealt *su, double eps) {
MSKint32t i;
for(i = 0; i < n; i++) {
if (fabs(sl[i]) > eps)
printf("#%d, lower, dual = %e\n", i, sl[i]);
if (fabs(su[i]) > eps)
printf("#%d, upper, dual = %e\n", i, su[i]);
}
}
int main(int argc, const char *argv[])
{
MSKtask_t task;
MSKrescodee r = MSK_RES_OK;
double inf = 0.0;
// In this example we set up a simple problem
// One could use any task or a task read from a file
r = testProblem(&task);
// Useful for debugging
if (r == MSK_RES_OK)
r = MSK_writedata(task, "pinfeas.ptf"); // Write file in human-readable format
// Directs the log task stream to the 'printstr' function.
if (r == MSK_RES_OK)
r = MSK_linkfunctotaskstream(task, MSK_STREAM_LOG, NULL, printstr);
// Perform the optimization.
if (r == MSK_RES_OK)
r = MSK_optimize(task);
if (r == MSK_RES_OK)
r = MSK_solutionsummary(task, MSK_STREAM_LOG);
// Check problem status, we use the interior point solution
{
MSKprostae prosta;
if (r == MSK_RES_OK)
r = MSK_getprosta(task, MSK_SOL_ITR, &prosta);
if (r == MSK_RES_OK && prosta == MSK_PRO_STA_PRIM_INFEAS) {
// Set the tolerance at which we consider a dual value as essential
double eps = 1e-7;
printf("Variable bounds important for infeasibility: \n");
if (r == MSK_RES_OK) {
MSKint32t m;
r = MSK_getnumvar(task, &m);
if (r == MSK_RES_OK) {
MSKrealt *slx = NULL, *sux = NULL;
slx = (MSKrealt*) calloc(m, sizeof(MSKrealt));
sux = (MSKrealt*) calloc(m, sizeof(MSKrealt));
if (r == MSK_RES_OK) r = MSK_getslx(task, MSK_SOL_ITR, slx);
if (r == MSK_RES_OK) r = MSK_getsux(task, MSK_SOL_ITR, sux);
if (r == MSK_RES_OK)
analyzeCertificate(m, slx, sux, eps);
free(sux);
free(slx);
}
}
printf("Constraint bounds important for infeasibility: \n");
if (r == MSK_RES_OK) {
MSKint32t n;
r = MSK_getnumcon(task, &n);
if (r == MSK_RES_OK) {
MSKrealt *slc = NULL, *suc = NULL;
slc = (MSKrealt*) calloc(n, sizeof(MSKrealt));
suc = (MSKrealt*) calloc(n, sizeof(MSKrealt));
if (r == MSK_RES_OK) r = MSK_getslc(task, MSK_SOL_ITR, slc);
if (r == MSK_RES_OK) r = MSK_getsuc(task, MSK_SOL_ITR, suc);
if (r == MSK_RES_OK)
analyzeCertificate(n, slc, suc, eps);
free(suc);
free(slc);
}
}
}
else {
printf("The problem is not primal infeasible, no certificate to show.\n");
}
}
MSK_deletetask(&task);
return r;
}
portfolio_1_basic.c
/*
File : portfolio_1_basic.c
Copyright : Copyright (c) MOSEK ApS, Denmark. All rights reserved.
Description : Implements a basic portfolio optimization model.
*/
#include <math.h>
#include <stdio.h>
#include "mosek.h"
#define MOSEKCALL(_r,_call) if ( (_r)==MSK_RES_OK ) (_r) = (_call)
static void MSKAPI printstr(void *handle,
const char str[])
{
printf("%s", str);
} /* printstr */
int main(int argc, const char **argv)
{
char buf[128];
double expret = 0.0,
stddev = 0.0,
xj;
const MSKint32t n = 8;
const MSKrealt gamma = 36.0;
const MSKrealt mu[] = {0.07197349, 0.15518171, 0.17535435, 0.0898094 , 0.42895777, 0.39291844, 0.32170722, 0.18378628};
// GT must have size n rows
const MSKrealt GT[][8] = {
{0.30758, 0.12146, 0.11341, 0.11327, 0.17625, 0.11973, 0.10435, 0.10638},
{0.0, 0.25042, 0.09946, 0.09164, 0.06692, 0.08706, 0.09173, 0.08506},
{0.0, 0.0, 0.19914, 0.05867, 0.06453, 0.07367, 0.06468, 0.01914},
{0.0, 0.0, 0.0, 0.20876, 0.04933, 0.03651, 0.09381, 0.07742},
{0.0, 0.0, 0.0, 0.0, 0.36096, 0.12574, 0.10157, 0.0571 },
{0.0, 0.0, 0.0, 0.0, 0.0, 0.21552, 0.05663, 0.06187},
{0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.22514, 0.03327},
{0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.2202 }
};
const MSKint32t k = sizeof(GT) / (n * sizeof(MSKrealt));
const MSKrealt x0[] = {8.0, 5.0, 3.0, 5.0, 2.0, 9.0, 3.0, 6.0};
const MSKrealt w = 59;
MSKrealt totalBudget;
MSKenv_t env;
MSKint32t i, j, *sub;
MSKrescodee res = MSK_RES_OK, trmcode;
MSKtask_t task;
//Offset of variables into the API variable.
MSKint32t numvar = n;
MSKint32t voff_x = 0;
// Constraints offsets
MSKint32t numcon = 1;
MSKint32t coff_bud = 0;
/* Initial setup. */
env = NULL;
task = NULL;
MOSEKCALL(res, MSK_makeenv(&env, NULL));
MOSEKCALL(res, MSK_maketask(env, 0, 0, &task));
MOSEKCALL(res, MSK_linkfunctotaskstream(task, MSK_STREAM_LOG, NULL, printstr));
// Holding variable x of length n
// No other auxiliary variables are needed in this formulation
MOSEKCALL(res, MSK_appendvars(task, numvar));
// Setting up variable x
for (j = 0; j < n; ++j)
{
/* Optionally we can give the variables names */
sprintf(buf, "x[%d]", 1 + j);
MOSEKCALL(res, MSK_putvarname(task, voff_x + j, buf));
/* No short-selling - x^l = 0, x^u = inf */
MOSEKCALL(res, MSK_putvarbound(task, voff_x + j, MSK_BK_LO, 0.0, MSK_INFINITY));
}
// One linear constraint: total budget
MOSEKCALL(res, MSK_appendcons(task, 1));
sprintf(buf, "%s", "budget");
MOSEKCALL(res, MSK_putconname(task, coff_bud, buf));
for (j = 0; j < n; ++j)
{
/* Coefficients in the first row of A */
MOSEKCALL(res, MSK_putaij(task, coff_bud, voff_x + j, 1.0));
}
totalBudget = w;
for (i = 0; i < n; ++i)
{
totalBudget += x0[i];
}
MOSEKCALL(res, MSK_putconbound(task, coff_bud, MSK_BK_FX, totalBudget, totalBudget));
// Input (gamma, GTx) in the AFE (affine expression) storage
// We need k+1 rows
MOSEKCALL(res, MSK_appendafes(task, k + 1));
// The first affine expression = gamma
MOSEKCALL(res, MSK_putafeg(task, 0, gamma));
// The remaining k expressions comprise GT*x, we add them row by row
// In more realisic scenarios it would be better to extract nonzeros and input in sparse form
MSKint32t* vslice_x = (MSKint32t*) malloc(n * sizeof(MSKint32t));
for (i = 0; i < n; ++i)
{
vslice_x[i] = voff_x + i;
}
for (i = 0; i < k; ++i)
{
MOSEKCALL(res, MSK_putafefrow(task, i + 1, n, vslice_x, GT[i]));
}
free(vslice_x);
// Input the affine conic constraint (gamma, GT*x) \in QCone
// Add the quadratic domain of dimension k+1
MSKint64t qdom;
MOSEKCALL(res, MSK_appendquadraticconedomain(task, k + 1, &qdom));
// Add the constraint
MOSEKCALL(res, MSK_appendaccseq(task, qdom, k + 1, 0, NULL));
sprintf(buf, "%s", "risk");
MOSEKCALL(res, MSK_putaccname(task, 0, buf));
// Objective: maximize expected return mu^T x
for (j = 0; j < n; ++j)
{
MOSEKCALL(res, MSK_putcj(task, voff_x + j, mu[j]));
}
MOSEKCALL(res, MSK_putobjsense(task, MSK_OBJECTIVE_SENSE_MAXIMIZE));
#if 0
/* No log output */
MOSEKCALL(res, MSK_putintparam(task, MSK_IPAR_LOG, 0));
#endif
#if 0
/* Dump the problem to a human readable PTF file. */
MOSEKCALL(res, MSK_writedata(task, "dump.ptf"));
#endif
MOSEKCALL(res, MSK_optimizetrm(task, &trmcode));
#if 1
/* Display the solution summary for quick inspection of results. */
MSK_solutionsummary(task, MSK_STREAM_MSG);
#endif
// Check if the interior point solution is an optimal point
MSKsolstae solsta;
MOSEKCALL(res, MSK_getsolsta(task, MSK_SOL_ITR, &solsta));
if (solsta != MSK_SOL_STA_OPTIMAL)
{
// See https://docs.mosek.com/latest/capi/accessing-solution.html about handling solution statuses.
fprintf(stderr, "Unexpected solution status: %d", solsta);
return MSK_RES_ERR_UNHANDLED_SOLUTION_STATUS;
}
if ( res == MSK_RES_OK )
{
expret = 0.0;
stddev = 0.0;
/* Read the x variables one by one and compute expected return. */
/* Can also be obtained as value of the objective. */
for (j = 0; j < n; ++j)
{
MOSEKCALL(res, MSK_getxxslice(task, MSK_SOL_ITR, voff_x + j, voff_x + j + 1, &xj));
expret += mu[j] * xj;
}
/* Read the value of s. This should be gamma. */
printf("\nExpected return %e for gamma %e\n", expret, gamma);
}
if ( task != NULL )
MSK_deletetask(&task);
if ( env != NULL )
MSK_deleteenv(&env);
return ( 0 );
}
portfolio_2_frontier.c
/*
File : portfolio_2_frontier.c
Copyright : Copyright (c) MOSEK ApS, Denmark. All rights reserved.
Description : Implements a basic portfolio optimization model.
Determines points on the efficient frontier.
*/
#include <math.h>
#include <stdio.h>
#include "mosek.h"
#define MOSEKCALL(_r,_call) if ( (_r)==MSK_RES_OK ) (_r) = (_call)
#define LOGLEVEL 0
static void MSKAPI printstr(void *handle,
const char str[])
{
printf("%s", str);
} /* printstr */
int main(int argc, const char **argv)
{
char buf[128];
const MSKint32t n = 8;
const MSKrealt mu[] = {0.07197349, 0.15518171, 0.17535435, 0.0898094 , 0.42895777, 0.39291844, 0.32170722, 0.18378628};
// GT must have size n rows
const MSKrealt GT[][8] = {
{0.30758, 0.12146, 0.11341, 0.11327, 0.17625, 0.11973, 0.10435, 0.10638},
{0.0, 0.25042, 0.09946, 0.09164, 0.06692, 0.08706, 0.09173, 0.08506},
{0.0, 0.0, 0.19914, 0.05867, 0.06453, 0.07367, 0.06468, 0.01914},
{0.0, 0.0, 0.0, 0.20876, 0.04933, 0.03651, 0.09381, 0.07742},
{0.0, 0.0, 0.0, 0.0, 0.36096, 0.12574, 0.10157, 0.0571 },
{0.0, 0.0, 0.0, 0.0, 0.0, 0.21552, 0.05663, 0.06187},
{0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.22514, 0.03327},
{0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.2202 }
};
const MSKint32t k = sizeof(GT) / (n * sizeof(MSKrealt));
const MSKrealt x0[] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
const MSKrealt w = 1.0;
const MSKrealt alphas[] = {0.0, 0.01, 0.1, 0.25, 0.30, 0.35, 0.4, 0.45, 0.5, 0.75, 1.0, 1.5, 2.0, 3.0, 10.0};
const MSKint32t numalpha = 15;
MSKrealt totalBudget;
MSKenv_t env;
MSKint32t i, j;
MSKrescodee res = MSK_RES_OK, lres;
MSKtask_t task;
MSKrealt xj;
MSKsolstae solsta;
//Offset of variables into the API variable.
MSKint32t numvar = n + 1;
MSKint32t voff_x = 0;
MSKint32t voff_s = n;
// Constraints offsets
MSKint32t numcon = 1;
MSKint32t coff_bud = 0;
/* Initial setup. */
env = NULL;
task = NULL;
/* Replace "" with NULL in production. */
MOSEKCALL(res, MSK_makeenv(&env, ""));
MOSEKCALL(res, MSK_maketask(env, 0, 0, &task));
MOSEKCALL(res, MSK_linkfunctotaskstream(task, MSK_STREAM_LOG, NULL, printstr));
// Holding variable x of length n
MOSEKCALL(res, MSK_appendvars(task, numvar));
// Setting up variable x
for (j = 0; j < n; ++j)
{
/* Optionally we can give the variables names */
sprintf(buf, "x[%d]", 1 + j);
MOSEKCALL(res, MSK_putvarname(task, voff_x + j, buf));
/* No short-selling - x^l = 0, x^u = inf */
MOSEKCALL(res, MSK_putvarbound(task, voff_x + j, MSK_BK_LO, 0.0, MSK_INFINITY));
}
sprintf(buf, "s");
MOSEKCALL(res, MSK_putvarname(task, voff_s, buf));
MOSEKCALL(res, MSK_putvarbound(task, voff_s, MSK_BK_FR, -MSK_INFINITY, MSK_INFINITY));
// One linear constraint: total budget
MOSEKCALL(res, MSK_appendcons(task, 1));
sprintf(buf, "%s", "budget");
MOSEKCALL(res, MSK_putconname(task, coff_bud, buf));
for (j = 0; j < n; ++j)
{
/* Coefficients in the first row of A */
MOSEKCALL(res, MSK_putaij(task, coff_bud, voff_x + j, 1.0));
}
totalBudget = w;
for (i = 0; i < n; ++i)
{
totalBudget += x0[i];
}
MOSEKCALL(res, MSK_putconbound(task, coff_bud, MSK_BK_FX, totalBudget, totalBudget));
// Input (gamma, GTx) in the AFE (affine expression) storage
// We build the following F and g for variables [x, s]:
// [0, 1] [0 ]
// F = [0, 0], g = [0.5]
// [GT,0] [0 ]
// We need k+2 rows
MOSEKCALL(res, MSK_appendafes(task, k + 2));
// The first affine expression is variable s (last variable, index n)
MOSEKCALL(res, MSK_putafefentry(task, 0, n, 1.0));
// The second affine expression is constant 0.5
MOSEKCALL(res, MSK_putafeg(task, 1, 0.5));
// The remaining k expressions comprise GT*x, we add them row by row
// In more realisic scenarios it would be better to extract nonzeros and input in sparse form
MSKint32t* vslice_x = (MSKint32t*) malloc(n * sizeof(MSKint32t));
for (i = 0; i < n; ++i)
{
vslice_x[i] = voff_x + i;
}
for (i = 0; i < k; ++i)
{
MOSEKCALL(res, MSK_putafefrow(task, i + 2, n, vslice_x, GT[i]));
}
free(vslice_x);
// Input the affine conic constraint (gamma, GT*x) \in QCone
// Add the quadratic domain of dimension k+1
MSKint64t rqdom;
MOSEKCALL(res, MSK_appendrquadraticconedomain(task, k + 2, &rqdom));
// Add the constraint
MOSEKCALL(res, MSK_appendaccseq(task, rqdom, k + 2, 0, NULL));
sprintf(buf, "%s", "risk");
MOSEKCALL(res, MSK_putaccname(task, 0, buf));
// Objective: maximize expected return mu^T x
for (j = 0; j < n; ++j)
{
MOSEKCALL(res, MSK_putcj(task, voff_x + j, mu[j]));
}
MOSEKCALL(res, MSK_putobjsense(task, MSK_OBJECTIVE_SENSE_MAXIMIZE));
/* Set the log level */
MOSEKCALL(res, MSK_putintparam(task, MSK_IPAR_LOG, LOGLEVEL));
printf("%-12s %-12s %-12s\n", "alpha", "exp ret", "std. dev");
for (i = 0; i < numalpha && res==MSK_RES_OK; ++i)
{
const double alpha = alphas[i];
MSKrescodee trmcode;
/* Sets the objective function coefficient for s. */
MOSEKCALL(res, MSK_putcj(task, voff_s + 0, -alpha));
MOSEKCALL(res, MSK_optimizetrm(task, &trmcode));
// Check if the interior point solution is an optimal point
MOSEKCALL(res, MSK_getsolsta(task, MSK_SOL_ITR, &solsta));
if (solsta != MSK_SOL_STA_OPTIMAL)
{
// See https://docs.mosek.com/latest/capi/accessing-solution.html about handling solution statuses.
fprintf(stderr, "Unexpected solution status: %d", solsta);
return MSK_RES_ERR_UNHANDLED_SOLUTION_STATUS;
}
if (solsta == MSK_SOL_STA_OPTIMAL)
{
double expret = 0.0,
stddev;
for (j = 0; j < n; ++j)
{
MOSEKCALL(res, MSK_getxxslice(task, MSK_SOL_ITR, voff_x + j, voff_x + j + 1, &xj));
expret += mu[j] * xj;
}
MOSEKCALL(res, MSK_getxxslice(task, MSK_SOL_ITR, voff_s + 0, voff_s + 1, &stddev));
printf("%-12.3e %-12.3e %-12.3e\n", alpha, expret, sqrt(stddev));
}
else
{
printf("An error occurred when solving for alpha=%e\n", alpha);
}
}
lres = MSK_deletetask(&task);
res = res==MSK_RES_OK ? lres : res;
lres = MSK_deleteenv(&env);
res = res==MSK_RES_OK ? lres : res;
return ( res );
}
portfolio_3_impact.c
/*
File : portfolio_3_impact.c
Copyright : Copyright (c) MOSEK ApS, Denmark. All rights reserved.
Description : Implements a basic portfolio optimization model
with transaction costs of order x^(3/2).
*/
#include <math.h>
#include <stdio.h>
#include "mosek.h"
#define MOSEKCALL(_r,_call) if ( (_r)==MSK_RES_OK ) (_r) = (_call)
static void MSKAPI printstr(void *handle,
const char str[])
{
printf("%s", str);
} /* printstr */
int main(int argc, const char **argv)
{
char buf[128];
const MSKint32t n = 8;
const MSKrealt mu[] = {0.07197, 0.15518, 0.17535, 0.08981, 0.42896, 0.39292, 0.32171, 0.18379};
// GT must have size n rows
const MSKrealt GT[][8] = {
{0.30758, 0.12146, 0.11341, 0.11327, 0.17625, 0.11973, 0.10435, 0.10638},
{0.0, 0.25042, 0.09946, 0.09164, 0.06692, 0.08706, 0.09173, 0.08506},
{0.0, 0.0, 0.19914, 0.05867, 0.06453, 0.07367, 0.06468, 0.01914},
{0.0, 0.0, 0.0, 0.20876, 0.04933, 0.03651, 0.09381, 0.07742},
{0.0, 0.0, 0.0, 0.0, 0.36096, 0.12574, 0.10157, 0.0571 },
{0.0, 0.0, 0.0, 0.0, 0.0, 0.21552, 0.05663, 0.06187},
{0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.22514, 0.03327},
{0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.2202 }
};
const MSKint32t k = sizeof(GT) / (n * sizeof(MSKrealt));
const MSKrealt x0[] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
const MSKrealt w = 1.0;
const MSKrealt gamma = 0.36;
MSKrealt totalBudget;
MSKint32t i, j;
MSKrealt* m = (MSKrealt*) malloc(n * sizeof(MSKrealt));
for (i = 0; i < n; ++i)
{
m[i] = 0.01;
}
// Offset of variables into the API variable.
MSKint32t numvar = 3 * n;
MSKint32t voff_x = 0;
MSKint32t voff_c = n;
MSKint32t voff_z = 2 * n;
// Offset of constraints.
MSKint32t numcon = 2 * n + 1;
MSKint32t coff_bud = 0;
MSKint32t coff_abs1 = 1;
MSKint32t coff_abs2 = 1 + n;
double expret,
stddev,
xj;
MSKenv_t env;
MSKrescodee res = MSK_RES_OK, trmcode;
MSKtask_t task;
/* Initial setup. */
env = NULL;
task = NULL;
MOSEKCALL(res, MSK_makeenv(&env, NULL));
MOSEKCALL(res, MSK_maketask(env, 0, 0, &task));
MOSEKCALL(res, MSK_linkfunctotaskstream(task, MSK_STREAM_LOG, NULL, printstr));
// Variables (vector of x, c, z)
MOSEKCALL(res, MSK_appendvars(task, numvar));
for (j = 0; j < n; ++j)
{
/* Optionally we can give the variables names */
sprintf(buf, "x[%d]", 1 + j);
MOSEKCALL(res, MSK_putvarname(task, voff_x + j, buf));
sprintf(buf, "c[%d]", 1 + j);
MOSEKCALL(res, MSK_putvarname(task, voff_c + j, buf));
sprintf(buf, "z[%d]", 1 + j);
MOSEKCALL(res, MSK_putvarname(task, voff_z + j, buf));
/* Apply variable bounds (x >= 0, c and z free) */
MOSEKCALL(res, MSK_putvarbound(task, voff_x + j, MSK_BK_LO, 0.0, MSK_INFINITY));
MOSEKCALL(res, MSK_putvarbound(task, voff_c + j, MSK_BK_FR, -MSK_INFINITY, MSK_INFINITY));
MOSEKCALL(res, MSK_putvarbound(task, voff_z + j, MSK_BK_FR, -MSK_INFINITY, MSK_INFINITY));
}
// Linear constraints
// - Total budget
MOSEKCALL(res, MSK_appendcons(task, 1));
sprintf(buf, "%s", "budget");
MOSEKCALL(res, MSK_putconname(task, coff_bud, buf));
for (j = 0; j < n; ++j)
{
/* Coefficients in the first row of A */
MOSEKCALL(res, MSK_putaij(task, coff_bud, voff_x + j, 1.0));
MOSEKCALL(res, MSK_putaij(task, coff_bud, voff_c + j, m[j]));
}
totalBudget = w;
for (i = 0; i < n; ++i)
{
totalBudget += x0[i];
}
MOSEKCALL(res, MSK_putconbound(task, coff_bud, MSK_BK_FX, totalBudget, totalBudget));
// - Absolute value
MOSEKCALL(res, MSK_appendcons(task, 2 * n));
for (i = 0; i < n; ++i)
{
sprintf(buf, "zabs1[%d]", 1 + i);
MOSEKCALL(res, MSK_putconname(task, coff_abs1 + i, buf));
MOSEKCALL(res, MSK_putaij(task, coff_abs1 + i, voff_x + i, -1.0));
MOSEKCALL(res, MSK_putaij(task, coff_abs1 + i, voff_z + i, 1.0));
MOSEKCALL(res, MSK_putconbound(task, coff_abs1 + i, MSK_BK_LO, -x0[i], MSK_INFINITY));
sprintf(buf, "zabs2[%d]", 1 + i);
MOSEKCALL(res, MSK_putconname(task, coff_abs2 + i, buf));
MOSEKCALL(res, MSK_putaij(task, coff_abs2 + i, voff_x + i, 1.0));
MOSEKCALL(res, MSK_putaij(task, coff_abs2 + i, voff_z + i, 1.0));
MOSEKCALL(res, MSK_putconbound(task, coff_abs2 + i, MSK_BK_LO, x0[i], MSK_INFINITY));
}
// ACCs
MSKint32t aoff_q = 0;
MSKint32t aoff_pow = k + 1;
// - (gamma, GTx) in Q(k+1)
// The part of F and g for variable x:
// [0, 0, 0] [gamma]
// F = [GT, 0, 0], g = [0 ]
MOSEKCALL(res, MSK_appendafes(task, k + 1));
MOSEKCALL(res, MSK_putafeg(task, aoff_q, gamma));
MSKint32t* vslice_x = (MSKint32t*) malloc(n * sizeof(MSKint32t));
for (i = 0; i < n; ++i)
{
vslice_x[i] = voff_x + i;
}
for (i = 0; i < k; ++i)
{
MOSEKCALL(res, MSK_putafefrow(task, aoff_q + i + 1, n, vslice_x, GT[i]));
}
free(vslice_x);
MSKint64t qdom;
MOSEKCALL(res, MSK_appendquadraticconedomain(task, k + 1, &qdom));
MOSEKCALL(res, MSK_appendaccseq(task, qdom, k + 1, aoff_q, NULL));
sprintf(buf, "%s", "risk");
MOSEKCALL(res, MSK_putaccname(task, aoff_q, buf));
// - (c_j, 1, z_j) in P3(2/3, 1/3)
// The part of F and g for variables [c, z]:
// [0, I, 0] [0]
// F = [0, 0, I], g = [0]
// [0, 0, 0] [1]
MOSEKCALL(res, MSK_appendafes(task, 2 * n + 1));
for (i = 0; i < n; ++i)
{
MOSEKCALL(res, MSK_putafefentry(task, aoff_pow + i, voff_c + i, 1.0));
MOSEKCALL(res, MSK_putafefentry(task, aoff_pow + n + i, voff_z + i, 1.0));
}
MOSEKCALL(res, MSK_putafeg(task, aoff_pow + 2 * n, 1.0));
// We use one row from F and g for both c_j and z_j, and the last row of F and g for the constant 1.
// NOTE: Here we reuse the last AFE and the power cone n times, but we store them only once.
MSKrealt exponents[] = {2, 1};
MSKint64t powdom;
MOSEKCALL(res, MSK_appendprimalpowerconedomain(task, 3, 2, exponents, &powdom));
MSKint64t* flat_afe_list = (MSKint64t*) malloc(3 * n * sizeof(MSKint64t));
MSKint64t* dom_list = (MSKint64t*) malloc(n * sizeof(MSKint64t));
for (i = 0; i < n; ++i)
{
flat_afe_list[3 * i + 0] = aoff_pow + i;
flat_afe_list[3 * i + 1] = aoff_pow + 2 * n;
flat_afe_list[3 * i + 2] = aoff_pow + n + i;
dom_list[i] = powdom;
}
MOSEKCALL(res, MSK_appendaccs(task, n, dom_list, 3 * n, flat_afe_list, NULL));
free(flat_afe_list);
free(dom_list);
for (i = 0; i < n; ++i)
{
sprintf(buf, "market_impact[%d]", i);
MOSEKCALL(res, MSK_putaccname(task, i + 1, buf));
}
// Objective: maximize expected return mu^T x
for (j = 0; j < n; ++j)
{
MOSEKCALL(res, MSK_putcj(task, voff_x + j, mu[j]));
}
MOSEKCALL(res, MSK_putobjsense(task, MSK_OBJECTIVE_SENSE_MAXIMIZE));
#if 0
/* no log output. */
MOSEKCALL(res, MSK_putintparam(task, MSK_IPAR_LOG, 0));
#endif
#if 0
/* Dump the problem to a human readable OPF file. */
MOSEKCALL(res, MSK_writedata(task, "dump.ptf"));
#endif
MOSEKCALL(res, MSK_optimizetrm(task, &trmcode));
/* Display the solution summary for quick inspection of results. */
#if 1
MSK_solutionsummary(task, MSK_STREAM_MSG);
#endif
// Check if the interior point solution is an optimal point
MSKsolstae solsta;
MOSEKCALL(res, MSK_getsolsta(task, MSK_SOL_ITR, &solsta));
if (solsta != MSK_SOL_STA_OPTIMAL)
{
// See https://docs.mosek.com/latest/capi/accessing-solution.html about handling solution statuses.
fprintf(stderr, "Unexpected solution status: %d", solsta);
return MSK_RES_ERR_UNHANDLED_SOLUTION_STATUS;
}
if (res == MSK_RES_OK)
{
expret = 0.0;
stddev = 0.0;
for (j = 0; j < n; ++j)
{
MOSEKCALL(res, MSK_getxxslice(task, MSK_SOL_ITR, voff_x + j, voff_x + j + 1, &xj));
expret += mu[j] * xj;
}
printf("\nExpected return %e for gamma %e\n", expret, gamma);
}
MSK_deletetask(&task);
MSK_deleteenv(&env);
free(m);
return (0);
}
portfolio_4_transcost.c
/*
File : portfolio_4_transcost.c
Copyright : Copyright (c) MOSEK ApS, Denmark. All rights reserved.
Description : Implements a basic portfolio optimization model
with fixed setup costs and transaction costs
as a mixed-integer problem.
*/
#include <math.h>
#include <stdio.h>
#include "mosek.h"
#define MOSEKCALL(_r,_call) if ( (_r)==MSK_RES_OK ) (_r) = (_call)
static void MSKAPI printstr(void *handle,
const char str[])
{
printf("%s", str);
} /* printstr */
int main(int argc, const char **argv)
{
char buf[128];
const MSKint32t n = 8;
const MSKrealt mu[] = {0.07197, 0.15518, 0.17535, 0.08981, 0.42896, 0.39292, 0.32171, 0.18379};
// GT must have size n rows
const MSKrealt GT[][8] = {
{0.30758, 0.12146, 0.11341, 0.11327, 0.17625, 0.11973, 0.10435, 0.10638},
{0.0, 0.25042, 0.09946, 0.09164, 0.06692, 0.08706, 0.09173, 0.08506},
{0.0, 0.0, 0.19914, 0.05867, 0.06453, 0.07367, 0.06468, 0.01914},
{0.0, 0.0, 0.0, 0.20876, 0.04933, 0.03651, 0.09381, 0.07742},
{0.0, 0.0, 0.0, 0.0, 0.36096, 0.12574, 0.10157, 0.0571 },
{0.0, 0.0, 0.0, 0.0, 0.0, 0.21552, 0.05663, 0.06187},
{0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.22514, 0.03327},
{0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.2202 }
};
const MSKint32t k = sizeof(GT) / (n * sizeof(MSKrealt));
const MSKrealt x0[] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
const MSKrealt w = 1.0;
const MSKrealt gamma = 0.36;
MSKint32t i, j;
MSKrealt* f = (MSKrealt*) malloc(n * sizeof(MSKrealt));
MSKrealt* g = (MSKrealt*) malloc(n * sizeof(MSKrealt));
for (i = 0; i < n; ++i)
{
f[i] = 0.01;
g[i] = 0.001;
}
// Offset of variables.
MSKint32t numvar = 3 * n;
MSKint32t voff_x = 0;
MSKint32t voff_z = n;
MSKint32t voff_y = 2 * n;
// Offset of constraints.
MSKint32t numcon = 3 * n + 1;
MSKint32t coff_bud = 0;
MSKint32t coff_abs1 = 1;
MSKint32t coff_abs2 = 1 + n;
MSKint32t coff_swi = 1 + 2 * n;
double expret,
xj;
MSKenv_t env;
MSKrescodee res = MSK_RES_OK, trmcode;
MSKtask_t task;
/* Initial setup. */
env = NULL;
task = NULL;
MOSEKCALL(res, MSK_makeenv(&env, NULL));
MOSEKCALL(res, MSK_maketask(env, 0, 0, &task));
MOSEKCALL(res, MSK_linkfunctotaskstream(task, MSK_STREAM_LOG, NULL, printstr));
// Variables (vector of x, z, y)
MOSEKCALL(res, MSK_appendvars(task, numvar));
for (j = 0; j < n; ++j)
{
/* Optionally we can give the variables names */
sprintf(buf, "x[%d]", 1 + j);
MOSEKCALL(res, MSK_putvarname(task, voff_x + j, buf));
sprintf(buf, "z[%d]", 1 + j);
MOSEKCALL(res, MSK_putvarname(task, voff_z + j, buf));
sprintf(buf, "y[%d]", 1 + j);
MOSEKCALL(res, MSK_putvarname(task, voff_y + j, buf));
/* Apply variable bounds (x >= 0, z free, y binary) */
MOSEKCALL(res, MSK_putvarbound(task, voff_x + j, MSK_BK_LO, 0.0, MSK_INFINITY));
MOSEKCALL(res, MSK_putvarbound(task, voff_z + j, MSK_BK_FR, -MSK_INFINITY, MSK_INFINITY));
MOSEKCALL(res, MSK_putvarbound(task, voff_y + j, MSK_BK_RA, 0.0, 1.0));
MOSEKCALL(res, MSK_putvartype(task, voff_y + j, MSK_VAR_TYPE_INT));
}
// Linear constraints
// - Total budget
MOSEKCALL(res, MSK_appendcons(task, 1));
sprintf(buf, "%s", "budget");
MOSEKCALL(res, MSK_putconname(task, coff_bud, buf));
for (j = 0; j < n; ++j)
{
/* Coefficients in the first row of A */
MOSEKCALL(res, MSK_putaij(task, coff_bud, voff_x + j, 1.0));
MOSEKCALL(res, MSK_putaij(task, coff_bud, voff_z + j, g[j]));
MOSEKCALL(res, MSK_putaij(task, coff_bud, voff_y + j, f[j]));
}
MSKrealt U = w;
for (i = 0; i < n; ++i)
{
U += x0[i];
}
MOSEKCALL(res, MSK_putconbound(task, coff_bud, MSK_BK_FX, U, U));
// - Absolute value
MOSEKCALL(res, MSK_appendcons(task, 2 * n));
for (i = 0; i < n; ++i)
{
sprintf(buf, "zabs1[%d]", 1 + i);
MOSEKCALL(res, MSK_putconname(task, coff_abs1 + i, buf));
MOSEKCALL(res, MSK_putaij(task, coff_abs1 + i, voff_x + i, -1.0));
MOSEKCALL(res, MSK_putaij(task, coff_abs1 + i, voff_z + i, 1.0));
MOSEKCALL(res, MSK_putconbound(task, coff_abs1 + i, MSK_BK_LO, -x0[i], MSK_INFINITY));
sprintf(buf, "zabs2[%d]", 1 + i);
MOSEKCALL(res, MSK_putconname(task, coff_abs2 + i, buf));
MOSEKCALL(res, MSK_putaij(task, coff_abs2 + i, voff_x + i, 1.0));
MOSEKCALL(res, MSK_putaij(task, coff_abs2 + i, voff_z + i, 1.0));
MOSEKCALL(res, MSK_putconbound(task, coff_abs2 + i, MSK_BK_LO, x0[i], MSK_INFINITY));
}
// - Switch
MOSEKCALL(res, MSK_appendcons(task, n));
for (i = 0; i < n; ++i)
{
sprintf(buf, "switch[%d]", 1 + i);
MOSEKCALL(res, MSK_putconname(task, coff_swi + i, buf));
MOSEKCALL(res, MSK_putaij(task, coff_swi + i, voff_z + i, 1.0));
MOSEKCALL(res, MSK_putaij(task, coff_swi + i, voff_y + i, -U));
MOSEKCALL(res, MSK_putconbound(task, coff_swi + i, MSK_BK_UP, -MSK_INFINITY, 0.0));
}
// ACCs
MSKint32t aoff_q = 0;
// - (gamma, GTx) in Q(k+1)
// The part of F and g for variable x:
// [0, 0, 0] [gamma]
// F = [GT, 0, 0], g = [0 ]
MOSEKCALL(res, MSK_appendafes(task, k + 1));
MOSEKCALL(res, MSK_putafeg(task, aoff_q, gamma));
MSKint32t* vslice_x = (MSKint32t*) malloc(n * sizeof(MSKint32t));
for (i = 0; i < n; ++i)
{
vslice_x[i] = voff_x + i;
}
for (i = 0; i < k; ++i)
{
MOSEKCALL(res, MSK_putafefrow(task, aoff_q + i + 1, n, vslice_x, GT[i]));
}
free(vslice_x);
MSKint64t qdom;
MOSEKCALL(res, MSK_appendquadraticconedomain(task, k + 1, &qdom));
MOSEKCALL(res, MSK_appendaccseq(task, qdom, k + 1, aoff_q, NULL));
sprintf(buf, "%s", "risk");
MOSEKCALL(res, MSK_putaccname(task, aoff_q, buf));
// Objective: maximize expected return mu^T x
for (j = 0; j < n; ++j)
{
MOSEKCALL(res, MSK_putcj(task, voff_x + j, mu[j]));
}
MOSEKCALL(res, MSK_putobjsense(task, MSK_OBJECTIVE_SENSE_MAXIMIZE));
#if 0
/* no log output. */
MOSEKCALL(res, MSK_putintparam(task, MSK_IPAR_LOG, 0));
#endif
#if 0
/* Dump the problem to a human readable OPF file. */
MOSEKCALL(res, MSK_writedata(task, "dump.ptf"));
#endif
MOSEKCALL(res, MSK_optimizetrm(task, &trmcode));
#if 1
/* Display the solution summary for quick inspection of results. */
MSK_solutionsummary(task, MSK_STREAM_MSG);
#endif
// Check if the interior point solution is an optimal point
MSKsolstae solsta;
MOSEKCALL(res, MSK_getsolsta(task, MSK_SOL_ITG, &solsta));
if (solsta != MSK_SOL_STA_INTEGER_OPTIMAL)
{
// See https://docs.mosek.com/latest/capi/accessing-solution.html about handling solution statuses.
fprintf(stderr, "Unexpected solution status: %d", solsta);
return MSK_RES_ERR_UNHANDLED_SOLUTION_STATUS;
}
if (res == MSK_RES_OK)
{
expret = 0.0;
for (j = 0; j < n; ++j)
{
MOSEKCALL(res, MSK_getxxslice(task, MSK_SOL_ITG, voff_x + j, voff_x + j + 1, &xj));
expret += mu[j] * xj;
}
printf("\nExpected return %e for gamma %e\n", expret, gamma);
}
MSK_deletetask(&task);
MSK_deleteenv(&env);
free(f);
free(g);
return (0);
}
portfolio_5_card.c
/*
File : portfolio_5_card.c
Copyright : Copyright (c) MOSEK ApS, Denmark. All rights reserved.
Description : Implements a basic portfolio optimization model
with cardinality constraints on number of assets traded.
*/
#include <math.h>
#include <stdio.h>
#include "mosek.h"
#define MOSEKCALL(_r,_call) if ( (_r)==MSK_RES_OK ) (_r) = (_call)
static void MSKAPI printstr(void *handle,
const char str[])
{
printf("%s", str);
} /* printstr */
MSKrescodee markowitz_with_card(const int n,
const int k,
const double x0[],
const double w,
const double gamma,
const double mu[],
const double GT[][8],
const int K,
double *xx)
{
// Offset of variables.
MSKint32t numvar = 3 * n;
MSKint32t voff_x = 0;
MSKint32t voff_z = n;
MSKint32t voff_y = 2 * n;
// Offset of constraints.
MSKint32t numcon = 3 * n + 2;
MSKint32t coff_bud = 0;
MSKint32t coff_abs1 = 1;
MSKint32t coff_abs2 = 1 + n;
MSKint32t coff_swi = 1 + 2 * n;
MSKint32t coff_card = 1 + 3 * n;
char buf[128];
MSKenv_t env;
MSKint32t i, j;
MSKrescodee res = MSK_RES_OK, trmcode;
MSKtask_t task;
/* Initial setup. */
env = NULL;
task = NULL;
MOSEKCALL(res, MSK_makeenv(&env, NULL));
MOSEKCALL(res, MSK_maketask(env, 0, 0, &task));
MOSEKCALL(res, MSK_linkfunctotaskstream(task, MSK_STREAM_LOG, NULL, printstr));
// Variables (vector of x, z, y)
MOSEKCALL(res, MSK_appendvars(task, numvar));
for (j = 0; j < n; ++j)
{
/* Optionally we can give the variables names */
sprintf(buf, "x[%d]", 1 + j);
MOSEKCALL(res, MSK_putvarname(task, voff_x + j, buf));
sprintf(buf, "z[%d]", 1 + j);
MOSEKCALL(res, MSK_putvarname(task, voff_z + j, buf));
sprintf(buf, "y[%d]", 1 + j);
MOSEKCALL(res, MSK_putvarname(task, voff_y + j, buf));
/* Apply variable bounds (x >= 0, z free, y binary) */
MOSEKCALL(res, MSK_putvarbound(task, voff_x + j, MSK_BK_LO, 0.0, MSK_INFINITY));
MOSEKCALL(res, MSK_putvarbound(task, voff_z + j, MSK_BK_FR, -MSK_INFINITY, MSK_INFINITY));
MOSEKCALL(res, MSK_putvarbound(task, voff_y + j, MSK_BK_RA, 0.0, 1.0));
MOSEKCALL(res, MSK_putvartype(task, voff_y + j, MSK_VAR_TYPE_INT));
}
// Linear constraints
// - Total budget
MOSEKCALL(res, MSK_appendcons(task, 1));
sprintf(buf, "%s", "budget");
MOSEKCALL(res, MSK_putconname(task, coff_bud, buf));
for (j = 0; j < n; ++j)
{
/* Coefficients in the first row of A */
MOSEKCALL(res, MSK_putaij(task, coff_bud, voff_x + j, 1.0));
}
MSKrealt U = w;
for (i = 0; i < n; ++i)
{
U += x0[i];
}
MOSEKCALL(res, MSK_putconbound(task, coff_bud, MSK_BK_FX, U, U));
// - Absolute value
MOSEKCALL(res, MSK_appendcons(task, 2 * n));
for (i = 0; i < n; ++i)
{
sprintf(buf, "zabs1[%d]", 1 + i);
MOSEKCALL(res, MSK_putconname(task, coff_abs1 + i, buf));
MOSEKCALL(res, MSK_putaij(task, coff_abs1 + i, voff_x + i, -1.0));
MOSEKCALL(res, MSK_putaij(task, coff_abs1 + i, voff_z + i, 1.0));
MOSEKCALL(res, MSK_putconbound(task, coff_abs1 + i, MSK_BK_LO, -x0[i], MSK_INFINITY));
sprintf(buf, "zabs2[%d]", 1 + i);
MOSEKCALL(res, MSK_putconname(task, coff_abs2 + i, buf));
MOSEKCALL(res, MSK_putaij(task, coff_abs2 + i, voff_x + i, 1.0));
MOSEKCALL(res, MSK_putaij(task, coff_abs2 + i, voff_z + i, 1.0));
MOSEKCALL(res, MSK_putconbound(task, coff_abs2 + i, MSK_BK_LO, x0[i], MSK_INFINITY));
}
// - Switch
MOSEKCALL(res, MSK_appendcons(task, n));
for (i = 0; i < n; ++i)
{
sprintf(buf, "switch[%d]", 1 + i);
MOSEKCALL(res, MSK_putconname(task, coff_swi + i, buf));
MOSEKCALL(res, MSK_putaij(task, coff_swi + i, voff_z + i, 1.0));
MOSEKCALL(res, MSK_putaij(task, coff_swi + i, voff_y + i, -U));
MOSEKCALL(res, MSK_putconbound(task, coff_swi + i, MSK_BK_UP, -MSK_INFINITY, 0.0));
}
// - Cardinality
MOSEKCALL(res, MSK_appendcons(task, 1));
sprintf(buf, "cardinality");
MOSEKCALL(res, MSK_putconname(task, coff_card, buf));
for (i = 0; i < n; ++i)
{
MOSEKCALL(res, MSK_putaij(task, coff_card, voff_y + i, 1.0));
MOSEKCALL(res, MSK_putconbound(task, coff_card, MSK_BK_UP, -MSK_INFINITY, K));
}
// ACCs
MSKint32t aoff_q = 0;
// - (gamma, GTx) in Q(k+1)
// The part of F and g for variable x:
// [0, 0, 0] [gamma]
// F = [GT, 0, 0], g = [0 ]
MOSEKCALL(res, MSK_appendafes(task, k + 1));
MOSEKCALL(res, MSK_putafeg(task, aoff_q, gamma));
MSKint32t* vslice_x = (MSKint32t*) malloc(n * sizeof(MSKint32t));
for (i = 0; i < n; ++i)
{
vslice_x[i] = voff_x + i;
}
for (i = 0; i < k; ++i)
{
MOSEKCALL(res, MSK_putafefrow(task, aoff_q + i + 1, n, vslice_x, GT[i]));
}
free(vslice_x);
MSKint64t qdom;
MOSEKCALL(res, MSK_appendquadraticconedomain(task, k + 1, &qdom));
MOSEKCALL(res, MSK_appendaccseq(task, qdom, k + 1, aoff_q, NULL));
sprintf(buf, "%s", "risk");
MOSEKCALL(res, MSK_putaccname(task, aoff_q, buf));
// Objective: maximize expected return mu^T x
for (j = 0; j < n; ++j)
{
MOSEKCALL(res, MSK_putcj(task, voff_x + j, mu[j]));
}
MOSEKCALL(res, MSK_putobjsense(task, MSK_OBJECTIVE_SENSE_MAXIMIZE));
#if 0
/* no log output. */
MOSEKCALL(res, MSK_putintparam(task, MSK_IPAR_LOG, 0));
#endif
#if 0
/* Dump the problem to a human readable OPF file. */
MOSEKCALL(res, MSK_writedata(task, "dump.ptf"));
#endif
MOSEKCALL(res, MSK_optimizetrm(task, &trmcode));
#if 1
/* Display the solution summary for quick inspection of results. */
MSK_solutionsummary(task, MSK_STREAM_MSG);
#endif
// Check if the interior point solution is an optimal point
MSKsolstae solsta;
MOSEKCALL(res, MSK_getsolsta(task, MSK_SOL_ITG, &solsta));
if (solsta != MSK_SOL_STA_INTEGER_OPTIMAL)
{
// See https://docs.mosek.com/latest/capi/accessing-solution.html about handling solution statuses.
fprintf(stderr, "Unexpected solution status: %d", solsta);
return MSK_RES_ERR_UNHANDLED_SOLUTION_STATUS;
}
if (res == MSK_RES_OK)
MOSEKCALL(res, MSK_getxxslice(task, MSK_SOL_ITG, voff_x, voff_x + n, xx));
MSK_deletetask(&task);
MSK_deleteenv(&env);
return res;
}
int main(int argc, const char **argv)
{
int i;
double expret;
MSKrescodee res;
const MSKint32t n = 8;
const MSKrealt mu[] = {0.07197, 0.15518, 0.17535, 0.08981, 0.42896, 0.39292, 0.32171, 0.18379};
// GT must have size n rows
const MSKrealt GT[][8] = {
{0.30758, 0.12146, 0.11341, 0.11327, 0.17625, 0.11973, 0.10435, 0.10638},
{0.0, 0.25042, 0.09946, 0.09164, 0.06692, 0.08706, 0.09173, 0.08506},
{0.0, 0.0, 0.19914, 0.05867, 0.06453, 0.07367, 0.06468, 0.01914},
{0.0, 0.0, 0.0, 0.20876, 0.04933, 0.03651, 0.09381, 0.07742},
{0.0, 0.0, 0.0, 0.0, 0.36096, 0.12574, 0.10157, 0.0571 },
{0.0, 0.0, 0.0, 0.0, 0.0, 0.21552, 0.05663, 0.06187},
{0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.22514, 0.03327},
{0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.2202 }
};
const MSKint32t k = sizeof(GT) / (n * sizeof(MSKrealt));
const MSKrealt x0[] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
const MSKrealt w = 1.0;
const MSKrealt gamma = 0.25;
double xx[] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
int K, j;
for (K = 1; K <= n; K++)
{
res = markowitz_with_card(n, k, x0, w, gamma, mu, GT, K, xx);
if (res == MSK_RES_OK)
{
expret = 0;
printf("Bound %d: x = ", K);
for(i=0; i<n; i++)
{
printf("%.5f ", xx[i]);
expret += xx[i]*mu[i];
}
printf(" Return: %.5f\n", expret);
}
}
return (0);
}
portfolio_6_factor.c
/*
File : portfolio_6_factor.c
Copyright : Copyright (c) MOSEK ApS, Denmark. All rights reserved.
Description : Implements a portfolio optimization model using factor model.
*/
#include <math.h>
#include <stdio.h>
#include "mosek.h"
#define MOSEKCALL(_r,_call) if ( (_r)==MSK_RES_OK ) (_r) = (_call)
static void MSKAPI printstr(void *handle,
const char str[])
{
printf("%s", str);
} /* printstr */
typedef struct
{
MSKrealt** m;
int nr;
int nc;
} matrix;
static void matrix_print(matrix* m)
{
int i,j;
for (i = 0; i < m->nr; ++i)
{
printf("[");
for (j = 0; j < m->nc; ++j)
{
printf("%f, ", m->m[i][j]);
}
printf("\b\b]\n");
}
}
static void array_print(MSKrealt* a, int len)
{
int j;
printf("[");
for (j = 0; j < len; ++j)
{
printf("%f, ", a[j]);
}
printf("\b\b]\n");
}
static matrix* matrix_alloc(int dim1, int dim2)
{
int i;
matrix* m = (matrix*) malloc(sizeof(matrix));
m->nr = dim1;
m->nc = dim2;
m->m = (MSKrealt**) malloc(dim1 * sizeof(MSKrealt*));
for (i = 0; i < dim1; ++i)
{
m->m[i] = (MSKrealt*) malloc(dim2 * sizeof(MSKrealt));
}
return m;
}
static void matrix_free(matrix* m)
{
int i;
for (i = 0; i < m->nr; ++i)
{
free(m->m[i]);
}
free(m->m);
free(m);
}
static MSKrealt* vector_alloc(int dim)
{
MSKrealt* v = (MSKrealt*) malloc(dim * sizeof(MSKrealt));
return v;
}
static void vector_free(MSKrealt* v)
{
free(v);
}
static MSKrealt sum(MSKrealt* x, int n)
{
int i;
MSKrealt r = 0.0;
for (i = 0; i < n; ++i) r += x[i];
return r;
}
static MSKrealt dot(MSKrealt* x, MSKrealt* y, int n)
{
int i;
MSKrealt r = 0.0;
for (i = 0; i < n; ++i) r += x[i] * y[i];
return r;
}
// Vectorize matrix (column-major order)
static MSKrealt* mat_to_vec_c(matrix* m)
{
int ni = m->nr;
int nj = m->nc;
int i,j;
MSKrealt* c = vector_alloc(ni * nj);
for (j = 0; j < nj; ++j)
{
for (i = 0; i < ni; ++i)
{
c[j * ni + i] = m->m[i][j];
}
}
return c;
}
// Reshape vector to matrix (column-major order)
static matrix* vec_to_mat_c(MSKrealt* c, int ni, int nj)
{
int i,j;
matrix* m = matrix_alloc(ni, nj);
for (j = 0; j < nj; ++j)
{
for (i = 0; i < ni; ++i)
{
m->m[i][j] = c[j * ni + i];
}
}
return m;
}
// Reshape vector to matrix (row-major order)
static matrix* vec_to_mat_r(MSKrealt* r, int ni, int nj)
{
int i,j;
matrix* m = matrix_alloc(ni, nj);
for (i = 0; i < ni; ++i)
{
for (j = 0; j < nj; ++j)
{
m->m[i][j] = r[i * nj + j];
}
}
return m;
}
static matrix* cholesky(MSKenv_t* env, matrix* m)
{
MSKrescodee res = MSK_RES_OK;
int i,j;
int n = m->nr;
MSKrealt* vecs = mat_to_vec_c(m);
MOSEKCALL(res, MSK_potrf(*env, MSK_UPLO_LO, n, vecs));
matrix* s = vec_to_mat_c(vecs, n, n);
vector_free(vecs);
// Zero out upper triangular part (MSK_potrf does not use it, original matrix values remain there)
for (i = 0; i < n; ++i)
{
for (j = i+1; j < n; ++j)
{
s->m[i][j] = 0.0;
}
}
return s;
}
// Matrix multiplication
static matrix* matrix_mul(MSKenv_t* env, matrix* a, matrix* b)
{
MSKrescodee res = MSK_RES_OK;
int na = a->nr;
int nb = b->nc;
int k = b->nr;
int i;
MSKrealt* vecm = vector_alloc(na * nb);
for (i = 0; i < na * nb; ++i) vecm[i] = 0.0;
MSKrealt* veca = mat_to_vec_c(a);
MSKrealt* vecb = mat_to_vec_c(b);
MOSEKCALL(res, MSK_gemm(*env, MSK_TRANSPOSE_NO, MSK_TRANSPOSE_NO, na, nb, k, 1.0, veca, vecb, 1.0, vecm));
vector_free(veca);
vector_free(vecb);
matrix* ab = vec_to_mat_c(vecm, na, nb);
vector_free(vecm);
return ab;
}
int main(int argc, const char **argv)
{
char buf[128];
MSKrealt expret = 0.0,
xj;
MSKrealt rtemp;
MSKenv_t env;
MSKint32t i, j, *sub;
MSKrescodee res = MSK_RES_OK, trmcode;
MSKtask_t task;
MSKint32t n = 8;
MSKrealt w = 1.0;
MSKrealt mu[] = {0.07197, 0.15518, 0.17535, 0.08981, 0.42896, 0.39292, 0.32171, 0.18379};
MSKrealt x0[] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
/* Initial setup. */
env = NULL;
task = NULL;
MOSEKCALL(res, MSK_makeenv(&env, NULL));
MOSEKCALL(res, MSK_maketask(env, 0, 0, &task));
MOSEKCALL(res, MSK_linkfunctotaskstream(task, MSK_STREAM_LOG, NULL, printstr));
// NOTE: Here we specify matrices as vectors (row major order) to avoid having
// to initialize them as double(*)[] type, which is incompatible with double**.
// Factor exposure matrix
MSKrealt vecB[] =
{
0.4256, 0.1869,
0.2413, 0.3877,
0.2235, 0.3697,
0.1503, 0.4612,
1.5325, -0.2633,
1.2741, -0.2613,
0.6939, 0.2372,
0.5425, 0.2116
};
matrix* B = vec_to_mat_r(vecB, n, 2);
// Factor covariance matrix
MSKrealt vecS_F[] =
{
0.0620, 0.0577,
0.0577, 0.0908
};
matrix* S_F = vec_to_mat_r(vecS_F, 2, 2);
// Specific risk components
MSKrealt theta[] = {0.0720, 0.0508, 0.0377, 0.0394, 0.0663, 0.0224, 0.0417, 0.0459};
matrix* P = cholesky(&env, S_F);
matrix* G_factor = matrix_mul(&env, B, P);
matrix_free(B);
matrix_free(S_F);
matrix_free(P);
MSKint32t k = G_factor->nc;
MSKrealt gammas[] = {0.24, 0.28, 0.32, 0.36, 0.4, 0.44, 0.48};
int num_gammas = 7;
MSKrealt totalBudget;
//Offset of variables into the API variable.
MSKint32t numvar = n;
MSKint32t voff_x = 0;
// Constraint offset
MSKint32t coff_bud = 0;
// Holding variable x of length n
// No other auxiliary variables are needed in this formulation
MOSEKCALL(res, MSK_appendvars(task, numvar));
// Setting up variable x
for (j = 0; j < n; ++j)
{
/* Optionally we can give the variables names */
sprintf(buf, "x[%d]", 1 + j);
MOSEKCALL(res, MSK_putvarname(task, voff_x + j, buf));
/* No short-selling - x^l = 0, x^u = inf */
MOSEKCALL(res, MSK_putvarbound(task, voff_x + j, MSK_BK_LO, 0.0, MSK_INFINITY));
}
// One linear constraint: total budget
MOSEKCALL(res, MSK_appendcons(task, 1));
sprintf(buf, "%s", "budget");
MOSEKCALL(res, MSK_putconname(task, coff_bud, buf));
for (j = 0; j < n; ++j)
{
/* Coefficients in the first row of A */
MOSEKCALL(res, MSK_putaij(task, coff_bud, voff_x + j, 1.0));
}
totalBudget = w;
for (i = 0; i < n; ++i)
{
totalBudget += x0[i];
}
MOSEKCALL(res, MSK_putconbound(task, coff_bud, MSK_BK_FX, totalBudget, totalBudget));
// Input (gamma, G_factor_T x, diag(sqrt(theta))*x) in the AFE (affine expression) storage
// We need k+n+1 rows and we fill them in in three parts
MOSEKCALL(res, MSK_appendafes(task, k + n + 1));
// 1. The first affine expression = gamma, will be specified later
// 2. The next k expressions comprise G_factor_T*x, we add them column by column since
// G_factor is stored row-wise and we transpose on the fly
MSKint64t* afeidxs = (MSKint64t*) malloc(k * sizeof(MSKint64t));
for (i = 0; i < k; ++i)
{
afeidxs[i] = i + 1;
}
for (i = 0; i < n; ++i)
{
MOSEKCALL(res, MSK_putafefcol(task, i, k, afeidxs, G_factor->m[i])); //i-th row of G_factor goes in i-th column of F
}
free(afeidxs);
// 3. The remaining n rows contain sqrt(theta) on the diagonal
for (i = 0; i < n; ++i)
{
MOSEKCALL(res, MSK_putafefentry(task, k + 1 + i, voff_x + i, sqrt(theta[i])));
}
// Input the affine conic constraint (gamma, G_factor_T x, diag(sqrt(theta))*x) \in QCone
// Add the quadratic domain of dimension k+n+1
MSKint64t qdom;
MOSEKCALL(res, MSK_appendquadraticconedomain(task, k + n + 1, &qdom));
// Add the constraint
MOSEKCALL(res, MSK_appendaccseq(task, qdom, k + n + 1, 0, NULL));
sprintf(buf, "%s", "risk");
MOSEKCALL(res, MSK_putaccname(task, 0, buf));
// Objective: maximize expected return mu^T x
for (j = 0; j < n; ++j)
{
MOSEKCALL(res, MSK_putcj(task, voff_x + j, mu[j]));
}
MOSEKCALL(res, MSK_putobjsense(task, MSK_OBJECTIVE_SENSE_MAXIMIZE));
#if 0
/* No log output */
MOSEKCALL(res, MSK_putintparam(task, MSK_IPAR_LOG, 0));
#endif
for (i = 0; i < num_gammas; i++)
{
MSKrealt gamma = gammas[i];
// Specify gamma in ACC
MOSEKCALL(res, MSK_putafeg(task, 0, gamma));
#if 0
/* Dump the problem to a human readable PTF file. */
MOSEKCALL(res, MSK_writedata(task, "dump.ptf"));
#endif
MOSEKCALL(res, MSK_optimizetrm(task, &trmcode));
#if 1
/* Display the solution summary for quick inspection of results. */
MSK_solutionsummary(task, MSK_STREAM_MSG);
#endif
// Check if the interior point solution is an optimal point
MSKsolstae solsta;
MOSEKCALL(res, MSK_getsolsta(task, MSK_SOL_ITR, &solsta));
if (solsta != MSK_SOL_STA_OPTIMAL)
{
// See https://docs.mosek.com/latest/capi/accessing-solution.html about handling solution statuses.
fprintf(stderr, "Unexpected solution status: %d", solsta);
return MSK_RES_ERR_UNHANDLED_SOLUTION_STATUS;
}
if ( res == MSK_RES_OK )
{
expret = 0.0;
/* Read the x variables one by one and compute expected return. */
/* Can also be obtained as value of the objective. */
for (j = 0; j < n; ++j)
{
MOSEKCALL(res, MSK_getxxslice(task, MSK_SOL_ITR, voff_x + j, voff_x + j + 1, &xj));
expret += mu[j] * xj;
}
printf("\nExpected return %e for gamma %e\n", expret, gamma);
}
}
if ( task != NULL )
MSK_deletetask(&task);
if ( env != NULL )
MSK_deleteenv(&env);
matrix_free(G_factor);
return ( 0 );
}
pow1.c
/*
Copyright: Copyright (c) MOSEK ApS, Denmark. All rights reserved.
File: pow1.c
Purpose: Demonstrates how to solve the problem
maximize x^0.2*y^0.8 + z^0.4 - x
st x + y + 0.5z = 2
x,y,z >= 0
*/
#include <stdio.h>
#include "mosek.h" /* Include the MOSEK definition file. */
static void MSKAPI printstr(void *handle,
const char str[])
{
printf("%s", str);
} /* printstr */
int main(int argc, const char *argv[])
{
MSKrescodee r;
const MSKint32t numvar = 5,
numcon = 1;
const MSKint64t numafe = 6,
numacc = 2,
f_nnz = 5;
MSKboundkeye bkx[5];
double blx[5], bux[5];
double val[] = { 1.0, 1.0, -1.0 };
MSKint32t sub[] = { 3, 4, 0 };
double aval[] = { 1.0, 1.0, 0.5 };
MSKint32t asub[] = { 0, 1, 2 };
MSKint64t afeidx[] = {0, 1, 2, 3, 5};
MSKint32t varidx[] = {0, 1, 3, 2, 4};
MSKrealt f_val[] = {1, 1, 1, 1, 1},
g = 1;
const MSKrealt alpha_1[]= {0.2, 0.8},
alpha_2[]= {0.4, 0.6};
MSKint64t domidx[] = {0, 0};
MSKint32t i, j;
MSKenv_t env = NULL;
MSKtask_t task = NULL;
/* Create the mosek environment. */
r = MSK_makeenv(&env, NULL);
if (r == MSK_RES_OK)
{
/* Create the optimization task. */
r = MSK_maketask(env, numcon, numvar, &task);
if (r == MSK_RES_OK)
{
MSK_linkfunctotaskstream(task, MSK_STREAM_LOG, NULL, printstr);
/* Append 'numcon' empty constraints.
The constraints will initially have no bounds. */
if (r == MSK_RES_OK)
r = MSK_appendcons(task, numcon);
/* Append 'numvar' variables.
The variables will initially be fixed at zero (x=0). */
if (r == MSK_RES_OK)
r = MSK_appendvars(task, numvar);
/* Append 'numafe' affine expressions.
The affine expressions will initially be empty. */
if (r == MSK_RES_OK)
r = MSK_appendafes(task, numafe);
/* Set up the linear part */
MSK_putclist(task, 3, sub, val);
MSK_putarow(task, 0, 3, asub, aval);
MSK_putconbound(task, 0, MSK_BK_FX, 2.0, 2.0);
for(i=0;i<5;i++)
bkx[i] = MSK_BK_FR, blx[i] = -MSK_INFINITY, bux[i] = MSK_INFINITY;
MSK_putvarboundslice(task, 0, numvar, bkx, blx, bux);
if (r == MSK_RES_OK)
{
/* Set the non-zero entries of the F matrix */
r = MSK_putafefentrylist(task, f_nnz, afeidx, varidx, f_val);
/* Set the non-zero element of the g vector */
if (r == MSK_RES_OK)
r = MSK_putafeg(task, 4, g);
/* Append the primal power cone domains with their respective parameter values. */
if (r == MSK_RES_OK)
r = MSK_appendprimalpowerconedomain(task, 3, 2, alpha_1, domidx);
if (r == MSK_RES_OK)
r = MSK_appendprimalpowerconedomain(task, 3, 2, alpha_2, domidx+1);
/* Append two ACCs made up of the AFEs and the domains defined above. */
if (r == MSK_RES_OK)
r = MSK_appendaccsseq(task, numacc, domidx, numafe, afeidx[0], NULL);
}
MSK_putobjsense(task, MSK_OBJECTIVE_SENSE_MAXIMIZE);
if (r == MSK_RES_OK)
{
MSKrescodee trmcode;
/* Run optimizer */
r = MSK_optimizetrm(task, &trmcode);
/* Print a summary containing information
about the solution for debugging purposes*/
MSK_solutionsummary(task, MSK_STREAM_MSG);
if (r == MSK_RES_OK)
{
MSKsolstae solsta;
MSK_getsolsta(task, MSK_SOL_ITR, &solsta);
switch (solsta)
{
case MSK_SOL_STA_OPTIMAL:
{
double *xx = NULL;
xx = calloc(numvar, sizeof(double));
if (xx)
{
MSK_getxx(task,
MSK_SOL_ITR, /* Request the interior solution. */
xx);
printf("Optimal primal solution\n");
for (j = 0; j < 3; ++j)
printf("x[%d]: %e\n", j, xx[j]);
}
else
{
r = MSK_RES_ERR_SPACE;
}
free(xx);
}
break;
case MSK_SOL_STA_DUAL_INFEAS_CER:
case MSK_SOL_STA_PRIM_INFEAS_CER:
printf("Primal or dual infeasibility certificate found.\n");
break;
case MSK_SOL_STA_UNKNOWN:
printf("The status of the solution could not be determined. Termination code: %d.\n", trmcode);
break;
default:
printf("Other solution status.");
break;
}
}
else
{
printf("Error while optimizing.\n");
}
}
if (r != MSK_RES_OK)
{
/* In case of an error print error code and description. */
char symname[MSK_MAX_STR_LEN];
char desc[MSK_MAX_STR_LEN];
printf("An error occurred while optimizing.\n");
MSK_getcodedesc(r,
symname,
desc);
printf("Error %s - '%s'\n", symname, desc);
}
}
/* Delete the task and the associated data. */
MSK_deletetask(&task);
}
/* Delete the environment and the associated data. */
MSK_deleteenv(&env);
return (r);
} /* main */
qcqo1.c
/*
Copyright: Copyright (c) MOSEK ApS, Denmark. All rights reserved.
File: qcqo1.c
Purpose: To demonstrate how to solve a quadratic
optimization problem using the MOSEK API.
minimize x_1^2 + 0.1 x_2^2 + x_3^2 - x_1 x_3 - x_2
s.t 1 <= x_1 + x_2 + x_3 - x_1^2 - x_2^2 - 0.1 x_3^2 + 0.2 x_1 x_3
x >= 0
*/
#include <stdio.h>
#include "mosek.h" /* Include the MOSEK definition file. */
#define NUMCON 1 /* Number of constraints. */
#define NUMVAR 3 /* Number of variables. */
#define NUMANZ 3 /* Number of non-zeros in A. */
#define NUMQNZ 4 /* Number of non-zeros in Q. */
static void MSKAPI printstr(void *handle,
const char str[])
{
printf("%s", str);
} /* printstr */
int main(int argc, const char *argv[])
{
MSKrescodee r;
double c[] = {0.0, -1.0, 0.0};
MSKboundkeye bkc[] = {MSK_BK_LO};
double blc[] = {1.0};
double buc[] = { +MSK_INFINITY};
MSKboundkeye bkx[] = {MSK_BK_LO,
MSK_BK_LO,
MSK_BK_LO
};
double blx[] = {0.0,
0.0,
0.0
};
double bux[] = { +MSK_INFINITY,
+MSK_INFINITY,
+MSK_INFINITY
};
MSKint32t aptrb[] = {0, 1, 2 },
aptre[] = {1, 2, 3},
asub[] = { 0, 0, 0};
double aval[] = { 1.0, 1.0, 1.0};
MSKint32t qsubi[NUMQNZ],
qsubj[NUMQNZ];
double qval[NUMQNZ];
MSKint32t j, i;
double xx[NUMVAR];
MSKenv_t env;
MSKtask_t task;
/* Create the mosek environment. */
r = MSK_makeenv(&env, NULL);
if (r == MSK_RES_OK)
{
/* Create the optimization task. */
r = MSK_maketask(env, NUMCON, NUMVAR, &task);
if (r == MSK_RES_OK)
{
r = MSK_linkfunctotaskstream(task, MSK_STREAM_LOG, NULL, printstr);
/* Append 'NUMCON' empty constraints.
The constraints will initially have no bounds. */
if (r == MSK_RES_OK)
r = MSK_appendcons(task, NUMCON);
/* Append 'NUMVAR' variables.
The variables will initially be fixed at zero (x=0). */
if (r == MSK_RES_OK)
r = MSK_appendvars(task, NUMVAR);
/* Optionally add a constant term to the objective. */
if (r == MSK_RES_OK)
r = MSK_putcfix(task, 0.0);
for (j = 0; j < NUMVAR && r == MSK_RES_OK; ++j)
{
/* Set the linear term c_j in the objective.*/
if (r == MSK_RES_OK)
r = MSK_putcj(task, j, c[j]);
/* Set the bounds on variable j.
blx[j] <= x_j <= bux[j] */
if (r == MSK_RES_OK)
r = MSK_putvarbound(task,
j, /* Index of variable.*/
bkx[j], /* Bound key.*/
blx[j], /* Numerical value of lower bound.*/
bux[j]); /* Numerical value of upper bound.*/
/* Input column j of A */
if (r == MSK_RES_OK)
r = MSK_putacol(task,
j, /* Variable (column) index.*/
aptre[j] - aptrb[j], /* Number of non-zeros in column j.*/
asub + aptrb[j], /* Pointer to row indexes of column j.*/
aval + aptrb[j]); /* Pointer to Values of column j.*/
}
/* Set the bounds on constraints.
for i=1, ...,NUMCON : blc[i] <= constraint i <= buc[i] */
for (i = 0; i < NUMCON && r == MSK_RES_OK; ++i)
r = MSK_putconbound(task,
i, /* Index of constraint.*/
bkc[i], /* Bound key.*/
blc[i], /* Numerical value of lower bound.*/
buc[i]); /* Numerical value of upper bound.*/
if (r == MSK_RES_OK)
{
/*
* The lower triangular part of the Q^o
* matrix in the objective is specified.
*/
qsubi[0] = 0; qsubj[0] = 0; qval[0] = 2.0;
qsubi[1] = 1; qsubj[1] = 1; qval[1] = 0.2;
qsubi[2] = 2; qsubj[2] = 0; qval[2] = -1.0;
qsubi[3] = 2; qsubj[3] = 2; qval[3] = 2.0;
/* Input the Q^o for the objective. */
r = MSK_putqobj(task, NUMQNZ, qsubi, qsubj, qval);
}
if (r == MSK_RES_OK)
{
/*
* The lower triangular part of the Q^0
* matrix in the first constraint is specified.
This corresponds to adding the term
- x_1^2 - x_2^2 - 0.1 x_3^2 + 0.2 x_1 x_3
*/
qsubi[0] = 0; qsubj[0] = 0; qval[0] = -2.0;
qsubi[1] = 1; qsubj[1] = 1; qval[1] = -2.0;
qsubi[2] = 2; qsubj[2] = 2; qval[2] = -0.2;
qsubi[3] = 2; qsubj[3] = 0; qval[3] = 0.2;
/* Put Q^0 in constraint with index 0. */
r = MSK_putqconk(task,
0,
4,
qsubi,
qsubj,
qval);
}
if (r == MSK_RES_OK)
r = MSK_putobjsense(task, MSK_OBJECTIVE_SENSE_MINIMIZE);
if (r == MSK_RES_OK)
{
MSKrescodee trmcode;
/* Run optimizer */
r = MSK_optimizetrm(task, &trmcode);
/* Print a summary containing information
about the solution for debugging purposes*/
MSK_solutionsummary(task, MSK_STREAM_LOG);
if (r == MSK_RES_OK)
{
MSKsolstae solsta;
int j;
MSK_getsolsta(task, MSK_SOL_ITR, &solsta);
switch (solsta)
{
case MSK_SOL_STA_OPTIMAL:
MSK_getxx(task,
MSK_SOL_ITR, /* Request the interior solution. */
xx);
printf("Optimal primal solution\n");
for (j = 0; j < NUMVAR; ++j)
printf("x[%d]: %e\n", j, xx[j]);
break;
case MSK_SOL_STA_DUAL_INFEAS_CER:
case MSK_SOL_STA_PRIM_INFEAS_CER:
printf("Primal or dual infeasibility certificate found.\n");
break;
case MSK_SOL_STA_UNKNOWN:
printf("The status of the solution could not be determined. Termination code: %d.\n", trmcode);
break;
default:
printf("Other solution status.");
break;
}
}
else
{
printf("Error while optimizing.\n");
}
}
if (r != MSK_RES_OK)
{
/* In case of an error print error code and description. */
char symname[MSK_MAX_STR_LEN];
char desc[MSK_MAX_STR_LEN];
printf("An error occurred while optimizing.\n");
MSK_getcodedesc(r,
symname,
desc);
printf("Error %s - '%s'\n", symname, desc);
}
}
MSK_deletetask(&task);
}
MSK_deleteenv(&env);
return (r);
} /* main */
qo1.c
/*
Copyright: Copyright (c) MOSEK ApS, Denmark. All rights reserved.
File: qo1.c
Purpose: To demonstrate how to solve a quadratic optimization
problem using the MOSEK API.
*/
#include <stdio.h>
#include "mosek.h" /* Include the MOSEK definition file. */
#define NUMCON 1 /* Number of constraints. */
#define NUMVAR 3 /* Number of variables. */
#define NUMANZ 3 /* Number of non-zeros in A. */
#define NUMQNZ 4 /* Number of non-zeros in Q. */
static void MSKAPI printstr(void *handle,
const char str[])
{
printf("%s", str);
} /* printstr */
int main(int argc, const char *argv[])
{
double c[] = {0.0, -1.0, 0.0};
MSKboundkeye bkc[] = {MSK_BK_LO};
double blc[] = {1.0};
double buc[] = { +MSK_INFINITY };
MSKboundkeye bkx[] = {MSK_BK_LO,
MSK_BK_LO,
MSK_BK_LO
};
double blx[] = {0.0,
0.0,
0.0
};
double bux[] = { +MSK_INFINITY,
+MSK_INFINITY,
+MSK_INFINITY
};
MSKint32t aptrb[] = {0, 1, 2},
aptre[] = {1, 2, 3},
asub[] = {0, 0, 0};
double aval[] = {1.0, 1.0, 1.0};
MSKint32t qsubi[NUMQNZ];
MSKint32t qsubj[NUMQNZ];
double qval[NUMQNZ];
MSKint32t i, j;
double xx[NUMVAR];
MSKenv_t env = NULL;
MSKtask_t task = NULL;
MSKrescodee r;
/* Create the mosek environment. */
r = MSK_makeenv(&env, NULL);
if (r == MSK_RES_OK)
{
/* Create the optimization task. */
r = MSK_maketask(env, NUMCON, NUMVAR, &task);
if (r == MSK_RES_OK)
{
r = MSK_linkfunctotaskstream(task, MSK_STREAM_LOG, NULL, printstr);
/* Append 'NUMCON' empty constraints.
The constraints will initially have no bounds. */
if (r == MSK_RES_OK)
r = MSK_appendcons(task, NUMCON);
/* Append 'NUMVAR' variables.
The variables will initially be fixed at zero (x=0). */
if (r == MSK_RES_OK)
r = MSK_appendvars(task, NUMVAR);
/* Optionally add a constant term to the objective. */
if (r == MSK_RES_OK)
r = MSK_putcfix(task, 0.0);
for (j = 0; j < NUMVAR && r == MSK_RES_OK; ++j)
{
/* Set the linear term c_j in the objective.*/
if (r == MSK_RES_OK)
r = MSK_putcj(task, j, c[j]);
/* Set the bounds on variable j.
blx[j] <= x_j <= bux[j] */
if (r == MSK_RES_OK)
r = MSK_putvarbound(task,
j, /* Index of variable.*/
bkx[j], /* Bound key.*/
blx[j], /* Numerical value of lower bound.*/
bux[j]); /* Numerical value of upper bound.*/
/* Input column j of A */
if (r == MSK_RES_OK)
r = MSK_putacol(task,
j, /* Variable (column) index.*/
aptre[j] - aptrb[j], /* Number of non-zeros in column j.*/
asub + aptrb[j], /* Pointer to row indexes of column j.*/
aval + aptrb[j]); /* Pointer to Values of column j.*/
}
/* Set the bounds on constraints.
for i=1, ...,NUMCON : blc[i] <= constraint i <= buc[i] */
for (i = 0; i < NUMCON && r == MSK_RES_OK; ++i)
r = MSK_putconbound(task,
i, /* Index of constraint.*/
bkc[i], /* Bound key.*/
blc[i], /* Numerical value of lower bound.*/
buc[i]); /* Numerical value of upper bound.*/
if (r == MSK_RES_OK)
{
/*
* The lower triangular part of the Q
* matrix in the objective is specified.
*/
qsubi[0] = 0; qsubj[0] = 0; qval[0] = 2.0;
qsubi[1] = 1; qsubj[1] = 1; qval[1] = 0.2;
qsubi[2] = 2; qsubj[2] = 0; qval[2] = -1.0;
qsubi[3] = 2; qsubj[3] = 2; qval[3] = 2.0;
/* Input the Q for the objective. */
r = MSK_putqobj(task, NUMQNZ, qsubi, qsubj, qval);
}
if (r == MSK_RES_OK)
{
MSKrescodee trmcode;
/* Run optimizer */
r = MSK_optimizetrm(task, &trmcode);
/* Print a summary containing information
about the solution for debugging purposes*/
MSK_solutionsummary(task, MSK_STREAM_MSG);
if (r == MSK_RES_OK)
{
MSKsolstae solsta;
int j;
MSK_getsolsta(task, MSK_SOL_ITR, &solsta);
switch (solsta)
{
case MSK_SOL_STA_OPTIMAL:
MSK_getxx(task,
MSK_SOL_ITR, /* Request the interior solution. */
xx);
printf("Optimal primal solution\n");
for (j = 0; j < NUMVAR; ++j)
printf("x[%d]: %e\n", j, xx[j]);
break;
case MSK_SOL_STA_DUAL_INFEAS_CER:
case MSK_SOL_STA_PRIM_INFEAS_CER:
printf("Primal or dual infeasibility certificate found.\n");
break;
case MSK_SOL_STA_UNKNOWN:
printf("The status of the solution could not be determined. Termination code: %d.\n", trmcode);
break;
default:
printf("Other solution status.");
break;
}
}
else
{
printf("Error while optimizing.\n");
}
}
if (r != MSK_RES_OK)
{
/* In case of an error print error code and description. */
char symname[MSK_MAX_STR_LEN];
char desc[MSK_MAX_STR_LEN];
printf("An error occurred while optimizing.\n");
MSK_getcodedesc(r,
symname,
desc);
printf("Error %s - '%s'\n", symname, desc);
}
}
MSK_deletetask(&task);
}
MSK_deleteenv(&env);
return (r);
} /* main */
reoptimization.c
/*
Copyright: Copyright (c) MOSEK ApS, Denmark. All rights reserved.
File: reoptimization.c
Purpose: To demonstrate how to solve a linear
optimization problem using the MOSEK API
and modify and re-optimize the problem.
*/
#include <stdio.h>
#define DEBUG 1 /* Set to zero to turn debugging off. */
#include "mosek.h" /* Include the MOSEK definition file. */
static void MSKAPI printstr(void *handle,
const char str[])
{
printf("%s", str);
} /* printstr */
void printres(int n, const double x[]) {
int i;
for (i = 0; i < n; i++) printf("%.3f ", x[i]);
printf("\n");
}
int main(int argc, char *argv[])
{
MSKint32t numvar = 3,
numcon = 3;
MSKint32t i, j;
double c[] = {1.5, 2.5, 3.0};
MSKint32t ptrb[] = {0, 3, 6},
ptre[] = {3, 6, 9},
asub[] = { 0, 1, 2,
0, 1, 2,
0, 1, 2
};
double aval[] = { 2.0, 3.0, 2.0,
4.0, 2.0, 3.0,
3.0, 3.0, 2.0
};
MSKboundkeye bkc[] = {MSK_BK_UP, MSK_BK_UP, MSK_BK_UP };
double blc[] = { -MSK_INFINITY, -MSK_INFINITY, -MSK_INFINITY};
double buc[] = {100000, 50000, 60000};
MSKboundkeye bkx[] = {MSK_BK_LO, MSK_BK_LO, MSK_BK_LO};
double blx[] = {0.0, 0.0, 0.0,};
double bux[] = { +MSK_INFINITY, +MSK_INFINITY, +MSK_INFINITY};
double *xx = NULL;
MSKenv_t env;
MSKtask_t task;
MSKint32t varidx, conidx;
MSKrescodee r,lr;
/* Create the mosek environment. */
r = MSK_makeenv(&env,DEBUG ? "" : NULL);
if (r == MSK_RES_OK)
{
/* Create the optimization task. */
r = MSK_maketask(env, numcon, numvar, &task);
/* Append the constraints. */
if (r == MSK_RES_OK)
r = MSK_appendcons(task, numcon);
/* Append the variables. */
if (r == MSK_RES_OK)
r = MSK_appendvars(task, numvar);
/* Put C. */
if (r == MSK_RES_OK)
r = MSK_putcfix(task, 0.0);
if (r == MSK_RES_OK)
for (j = 0; j < numvar; ++j)
r = MSK_putcj(task, j, c[j]);
/* Put constraint bounds. */
if (r == MSK_RES_OK)
for (i = 0; i < numcon; ++i)
r = MSK_putconbound(task, i, bkc[i], blc[i], buc[i]);
/* Put variable bounds. */
if (r == MSK_RES_OK)
for (j = 0; j < numvar; ++j)
r = MSK_putvarbound(task, j, bkx[j], blx[j], bux[j]);
/* Put A. */
if (r == MSK_RES_OK)
if (numcon > 0)
for (j = 0; j < numvar; ++j)
r = MSK_putacol(task,
j,
ptre[j] - ptrb[j],
asub + ptrb[j],
aval + ptrb[j]);
if (r == MSK_RES_OK)
r = MSK_putobjsense(task,
MSK_OBJECTIVE_SENSE_MAXIMIZE);
if (r == MSK_RES_OK)
r = MSK_optimizetrm(task, NULL);
if (r == MSK_RES_OK)
{
xx = calloc(numvar, sizeof(double));
if (!xx)
r = MSK_RES_ERR_SPACE;
}
if (r == MSK_RES_OK)
r = MSK_getxx(task,
MSK_SOL_BAS, /* Basic solution. */
xx);
printres(numvar, xx);
/******************** Make a change to the A matrix **********/
if (r == MSK_RES_OK)
r = MSK_putaij(task, 0, 0, 3.0);
if (r == MSK_RES_OK)
r = MSK_optimizetrm(task, NULL);
if (r == MSK_RES_OK)
r = MSK_getxx(task,
MSK_SOL_BAS, /* Basic solution. */
xx);
printres(numvar, xx);
if (xx)
free(xx);
/*********************** Add a new variable ******************/
/* Get index of new variable, this should be 3 */
if (r == MSK_RES_OK)
r = MSK_getnumvar(task, &varidx);
/* Append a new variable x_3 to the problem */
if (r == MSK_RES_OK)
{
r = MSK_appendvars(task, 1);
numvar++;
}
/* Set bounds on new variable */
if (r == MSK_RES_OK)
r = MSK_putvarbound(task,
varidx,
MSK_BK_LO,
0,
+MSK_INFINITY);
/* Change objective */
if (r == MSK_RES_OK)
r = MSK_putcj(task, varidx, 1.0);
/* Put new values in the A matrix */
if (r == MSK_RES_OK)
{
MSKint32t acolsub[] = {0, 2};
double acolval[] = {4.0, 1.0};
r = MSK_putacol(task,
varidx, /* column index */
2, /* num nz in column*/
acolsub,
acolval);
}
/* Change optimizer to free simplex and reoptimize */
if (r == MSK_RES_OK)
r = MSK_putintparam(task, MSK_IPAR_OPTIMIZER, MSK_OPTIMIZER_FREE_SIMPLEX);
if (r == MSK_RES_OK)
r = MSK_optimizetrm(task, NULL);
if (r == MSK_RES_OK)
{
xx = calloc(numvar, sizeof(double));
if (!xx)
r = MSK_RES_ERR_SPACE;
}
if (r == MSK_RES_OK)
r = MSK_getxx(task,
MSK_SOL_BAS, /* Basic solution. */
xx);
printres(numvar, xx);
/* **************** Add a new constraint ******************* */
/* Get index of new constraint*/
if (r == MSK_RES_OK)
r = MSK_getnumcon(task, &conidx);
/* Append a new constraint */
if (r == MSK_RES_OK)
{
r = MSK_appendcons(task, 1);
numcon++;
}
/* Set bounds on new constraint */
if (r == MSK_RES_OK)
r = MSK_putconbound(task,
conidx,
MSK_BK_UP,
-MSK_INFINITY,
30000);
/* Put new values in the A matrix */
if (r == MSK_RES_OK)
{
MSKint32t arowsub[] = {0, 1, 2, 3 };
double arowval[] = {1.0, 2.0, 1.0, 1.0};
r = MSK_putarow(task,
conidx, /* row index */
4, /* num nz in row*/
arowsub,
arowval);
}
if (r == MSK_RES_OK)
r = MSK_optimizetrm(task, NULL);
if (r == MSK_RES_OK)
r = MSK_getxx(task,
MSK_SOL_BAS, /* Basic solution. */
xx);
printres(numvar, xx);
/* **************** Change constraint bounds ******************* */
if (r == MSK_RES_OK)
{
MSKboundkeye newbkc[] = { MSK_BK_UP, MSK_BK_UP, MSK_BK_UP, MSK_BK_UP };
double newblc[] = { -MSK_INFINITY, -MSK_INFINITY, -MSK_INFINITY, -MSK_INFINITY };
double newbuc[] = { 80000, 40000, 50000, 22000 };
r = MSK_putconboundslice(task, 0, numcon, newbkc, newblc, newbuc);
}
if (r == MSK_RES_OK)
r = MSK_optimizetrm(task, NULL);
if (r == MSK_RES_OK)
r = MSK_getxx(task,
MSK_SOL_BAS, /* Basic solution. */
xx);
printres(numvar, xx);
if (xx)
free(xx);
lr = MSK_deletetask(&task);
if (r == MSK_RES_OK)
r = lr;
}
lr = MSK_deleteenv(&env);
if (r == MSK_RES_OK)
r = lr;
printf("Return code: %d (0 means no error occured.)\n", r);
return (r);
} /* main */
response.c
/*
Copyright: Copyright (c) MOSEK ApS, Denmark. All rights reserved.
File: response.c
Purpose: This example demonstrates proper response handling
for problems solved with the interior-point optimizers.
*/
#include <stdio.h>
#include "mosek.h"
/* Log handler */
void MSKAPI printlog(void *ptr,
const char s[])
{
printf("%s", s);
}
int main(int argc, char const *argv[])
{
MSKenv_t env;
MSKtask_t task;
MSKrescodee r;
char symname[MSK_MAX_STR_LEN];
char desc[MSK_MAX_STR_LEN];
int i, numvar;
double *xx = NULL;
const char *filename;
if (argc >= 2) filename = argv[1];
else filename = "../data/cqo1.mps";
// Create the environment
r = MSK_makeenv(&env, NULL);
if (r == MSK_RES_OK)
{
// Create the task
r = MSK_makeemptytask(env, &task);
// (Optionally) attach the log handler to receive log information
// if ( r == MSK_RES_OK ) MSK_linkfunctotaskstream(task, MSK_STREAM_LOG, NULL, printlog);
// (Optionally) uncomment this line to most likely see solution status Unknown
// MSK_putintparam(task, MSK_IPAR_INTPNT_MAX_ITERATIONS, 1);
// In this example we read an optimization problem from a file
r = MSK_readdata(task, filename);
if (r == MSK_RES_OK)
{
MSKrescodee trmcode;
MSKsolstae solsta;
// Do the optimization, and exit in case of error
r = MSK_optimizetrm(task, &trmcode);
if (r != MSK_RES_OK) {
MSK_getcodedesc(r, symname, desc);
printf("Error during optimization: %s %s\n", symname, desc);
exit(r);
}
MSK_solutionsummary(task, MSK_STREAM_LOG);
/* Expected result: The solution status of the interiot-point solution is optimal. */
if (MSK_RES_OK == MSK_getsolsta(task, MSK_SOL_ITR, &solsta))
{
switch (solsta)
{
case MSK_SOL_STA_OPTIMAL:
printf("An optimal interior-point solution is located.\n");
/* Read and print the variable values in the solution */
MSK_getnumvar(task, &numvar);
xx = calloc(numvar, sizeof(double));
MSK_getxx(task, MSK_SOL_ITR, xx);
for (i = 0; i < numvar; i++)
printf("xx[%d] = %.4lf\n", i, xx[i]);
free(xx);
break;
case MSK_SOL_STA_DUAL_INFEAS_CER:
printf("Dual infeasibility certificate found.\n");
break;
case MSK_SOL_STA_PRIM_INFEAS_CER:
printf("Primal infeasibility certificate found.\n");
break;
case MSK_SOL_STA_UNKNOWN:
/* The solutions status is unknown. The termination code
indicating why the optimizer terminated prematurely. */
printf("The solution status is unknown.\n");
/* No-error cause of termination e.g. an iteration limit is reached. */
MSK_getcodedesc(trmcode, symname, desc);
printf(" Termination code: %s %s\n", symname, desc);
break;
default:
MSK_solstatostr(task, solsta, desc);
printf("An unexpected solution status %s with code %d is obtained.\n", desc, solsta);
break;
}
}
else
printf("Could not obtain the solution status for the requested solution.\n");
}
else {
MSK_getcodedesc(r, symname, desc);
printf("Optimization was not started because of error %s(%d): %s\n", symname, r, desc);
}
MSK_deletetask(&task);
}
MSK_deleteenv(&env);
return r;
}
sdo1.c
/*
Copyright: Copyright (c) MOSEK ApS, Denmark. All rights reserved.
File: sdo1.c
Purpose: Solves the following small semidefinite optimization problem
using the MOSEK API.
minimize Tr [2, 1, 0; 1, 2, 1; 0, 1, 2]*X + x0
subject to Tr [1, 0, 0; 0, 1, 0; 0, 0, 1]*X + x0 = 1
Tr [1, 1, 1; 1, 1, 1; 1, 1, 1]*X + x1 + x2 = 0.5
(x0,x1,x2) \in Q, X \in PSD
*/
#include <stdio.h>
#include "mosek.h" /* Include the MOSEK definition file. */
#define NUMCON 2 /* Number of constraints. */
#define NUMVAR 3 /* Number of conic quadratic variables */
#define NUMANZ 3 /* Number of non-zeros in A */
#define NUMAFE 3 /* Number of affine expressions */
#define NUMFNZ 3 /* Number of non-zeros in F */
#define NUMBARVAR 1 /* Number of semidefinite variables */
static void MSKAPI printstr(void *handle,
const char str[])
{
printf("%s", str);
} /* printstr */
int main(int argc, const char *argv[])
{
MSKrescodee r;
MSKint32t DIMBARVAR[] = {3}; /* Dimension of semidefinite cone */
MSKint64t LENBARVAR[] = {3 * (3 + 1) / 2}; /* Number of scalar SD variables */
MSKboundkeye bkc[] = { MSK_BK_FX, MSK_BK_FX };
double blc[] = { 1.0, 0.5 };
double buc[] = { 1.0, 0.5 };
MSKint32t barc_i[] = {0, 1, 1, 2, 2},
barc_j[] = {0, 0, 1, 1, 2};
double barc_v[] = {2.0, 1.0, 2.0, 1.0, 2.0};
MSKint32t aptrb[] = {0, 1},
aptre[] = {1, 3},
asub[] = {0, 1, 2}; /* column subscripts of A */
double aval[] = {1.0, 1.0, 1.0};
MSKint32t bara_i[] = {0, 1, 2, 0, 1, 2, 1, 2, 2},
bara_j[] = {0, 1, 2, 0, 0, 0, 1, 1, 2};
double bara_v[] = {1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0};
MSKint32t conesub[] = {0, 1, 2};
MSKint64t afeidx[] = {0, 1, 2};
int varidx[] = {0, 1, 2};
double f_val[] = {1, 1, 1};
MSKint32t i, j;
MSKint64t idx;
double falpha = 1.0;
MSKrealt *xx;
MSKrealt *barx;
MSKenv_t env = NULL;
MSKtask_t task = NULL;
/* Create the mosek environment. */
r = MSK_makeenv(&env, NULL);
if (r == MSK_RES_OK)
{
/* Create the optimization task. */
r = MSK_maketask(env, NUMCON, 0, &task);
if (r == MSK_RES_OK)
{
MSK_linkfunctotaskstream(task, MSK_STREAM_LOG, NULL, printstr);
/* Append 'NUMCON' empty constraints.
The constraints will initially have no bounds. */
if (r == MSK_RES_OK)
r = MSK_appendcons(task, NUMCON);
/* Append 'NUMVAR' variables.
The variables will initially be fixed at zero (x=0). */
if (r == MSK_RES_OK)
r = MSK_appendvars(task, NUMVAR);
/* Append 'NUMAFE' affine expressions.*/
if (r == MSK_RES_OK)
r = MSK_appendafes(task, NUMAFE);
/* Append 'NUMBARVAR' semidefinite variables. */
if (r == MSK_RES_OK) {
r = MSK_appendbarvars(task, NUMBARVAR, DIMBARVAR);
}
/* Optionally add a constant term to the objective. */
if (r == MSK_RES_OK)
r = MSK_putcfix(task, 0.0);
/* Set the linear term c_j in the objective.*/
if (r == MSK_RES_OK)
r = MSK_putcj(task, 0, 1.0);
for (j = 0; j < NUMVAR && r == MSK_RES_OK; ++j)
r = MSK_putvarbound(task,
j,
MSK_BK_FR,
-MSK_INFINITY,
MSK_INFINITY);
/* Set the linear term barc_j in the objective.*/
if (r == MSK_RES_OK)
r = MSK_appendsparsesymmat(task,
DIMBARVAR[0],
5,
barc_i,
barc_j,
barc_v,
&idx);
if (r == MSK_RES_OK)
r = MSK_putbarcj(task, 0, 1, &idx, &falpha);
/* Set the bounds on constraints.
for i=1, ...,NUMCON : blc[i] <= constraint i <= buc[i] */
for (i = 0; i < NUMCON && r == MSK_RES_OK; ++i)
r = MSK_putconbound(task,
i, /* Index of constraint.*/
bkc[i], /* Bound key.*/
blc[i], /* Numerical value of lower bound.*/
buc[i]); /* Numerical value of upper bound.*/
/* Input A row by row */
for (i = 0; i < NUMCON && r == MSK_RES_OK; ++i)
r = MSK_putarow(task,
i,
aptre[i] - aptrb[i],
asub + aptrb[i],
aval + aptrb[i]);
/* Append the affine conic constraint with quadratic cone */
if (r == MSK_RES_OK)
{
r = MSK_putafefentrylist(task, NUMFNZ, afeidx, varidx, f_val);
if (r == MSK_RES_OK)
r = MSK_appendquadraticconedomain(task, 3, NULL);
if (r == MSK_RES_OK)
r = MSK_appendacc(task, 0, 3, afeidx, NULL);
}
/* Add the first row of barA */
if (r == MSK_RES_OK)
r = MSK_appendsparsesymmat(task,
DIMBARVAR[0],
3,
bara_i,
bara_j,
bara_v,
&idx);
if (r == MSK_RES_OK)
r = MSK_putbaraij(task, 0, 0, 1, &idx, &falpha);
/* Add the second row of barA */
if (r == MSK_RES_OK)
r = MSK_appendsparsesymmat(task,
DIMBARVAR[0],
6,
bara_i + 3,
bara_j + 3,
bara_v + 3,
&idx);
if (r == MSK_RES_OK)
r = MSK_putbaraij(task, 1, 0, 1, &idx, &falpha);
if (r == MSK_RES_OK)
{
MSKrescodee trmcode;
/* Run optimizer */
r = MSK_optimizetrm(task, &trmcode);
/* Print a summary containing information
about the solution for debugging purposes*/
MSK_solutionsummary(task, MSK_STREAM_MSG);
if (r == MSK_RES_OK)
{
MSKsolstae solsta;
MSK_getsolsta(task, MSK_SOL_ITR, &solsta);
switch (solsta)
{
case MSK_SOL_STA_OPTIMAL:
xx = (MSKrealt *) MSK_calloctask(task, NUMVAR, sizeof(MSKrealt));
barx = (MSKrealt *) MSK_calloctask(task, LENBARVAR[0], sizeof(MSKrealt));
MSK_getxx(task,
MSK_SOL_ITR,
xx);
MSK_getbarxj(task,
MSK_SOL_ITR, /* Request the interior solution. */
0,
barx);
printf("Optimal primal solution\n");
for (i = 0; i < NUMVAR; ++i)
printf("x[%d] : % e\n", i, xx[i]);
for (i = 0; i < LENBARVAR[0]; ++i)
printf("barx[%d]: % e\n", i, barx[i]);
MSK_freetask(task, xx);
MSK_freetask(task, barx);
break;
case MSK_SOL_STA_DUAL_INFEAS_CER:
case MSK_SOL_STA_PRIM_INFEAS_CER:
printf("Primal or dual infeasibility certificate found.\n");
break;
case MSK_SOL_STA_UNKNOWN:
printf("The status of the solution could not be determined. Termination code: %d.\n", trmcode);
break;
default:
printf("Other solution status.");
break;
}
}
else
{
printf("Error while optimizing.\n");
}
}
if (r != MSK_RES_OK)
{
/* In case of an error print error code and description. */
char symname[MSK_MAX_STR_LEN];
char desc[MSK_MAX_STR_LEN];
printf("An error occurred while optimizing.\n");
MSK_getcodedesc(r,
symname,
desc);
printf("Error %s - '%s'\n", symname, desc);
}
}
/* Delete the task and the associated data. */
MSK_deletetask(&task);
}
/* Delete the environment and the associated data. */
MSK_deleteenv(&env);
return (r);
} /* main */
sdo2.c
/*
Copyright : Copyright (c) MOSEK ApS, Denmark. All rights reserved.
File : sdo2.c
Purpose : Solves the semidefinite problem with two symmetric variables:
min <C1,X1> + <C2,X2>
st. <A1,X1> + <A2,X2> = b
(X2)_{1,2} <= k
where X1, X2 are symmetric positive semidefinite,
C1, C2, A1, A2 are assumed to be constant symmetric matrices,
and b, k are constants.
*/
#include <stdio.h>
#include "mosek.h" /* Include the MOSEK definition file. */
static void MSKAPI printstr(void *handle,
const char str[])
{
printf("%s", str);
} /* printstr */
int main(int argc, const char *argv[])
{
MSKrescodee r;
/* Input data */
MSKint32t numbarvar = 2;
MSKint32t dimbarvar[] = {3, 4}; /* Dimension of semidefinite variables */
/* Objective coefficients concatenated */
MSKint32t Cj[] = { 0, 0, 1, 1, 1, 1 }; /* Which symmetric variable (j) */
MSKint32t Ck[] = { 0, 2, 0, 1, 1, 2 }; /* Which entry (k,l)->v */
MSKint32t Cl[] = { 0, 2, 0, 0, 1, 2 };
MSKrealt Cv[] = { 1.0, 6.0, 1.0, -3.0, 2.0, 1.0 };
/* Equality constraints coefficients concatenated */
MSKint32t Ai[] = { 0, 0, 0, 0, 0, 0 }; /* Which constraint (i = 0) */
MSKint32t Aj[] = { 0, 0, 0, 1, 1, 1 }; /* Which symmetric variable (j) */
MSKint32t Ak[] = { 0, 2, 2, 1, 1, 3 }; /* Which entry (k,l)->v */
MSKint32t Al[] = { 0, 0, 2, 0, 1, 3 };
MSKrealt Av[] = { 1.0, 1.0, 2.0, 1.0, -1.0, -3.0 };
/* The second constraint - one-term inequality */
MSKint32t A2i = 1; /* Which constraint (i = 1) */
MSKint32t A2j = 1; /* Which symmetric variable (j = 1) */
MSKint32t A2k = 1; /* Which entry A(1,0) = A(0,1) = 0.5 */
MSKint32t A2l = 0;
MSKrealt A2v = 0.5;
/* Constraint bounds and values */
MSKint32t numcon = 2;
MSKboundkeye bkc[] = { MSK_BK_FX, MSK_BK_UP };
double blc[] = { 23.0, -MSK_INFINITY };
double buc[] = { 23.0, -3.0 };
MSKint32t i, j, dim;
MSKrealt *barx;
MSKenv_t env = NULL;
MSKtask_t task = NULL;
/* Create the mosek environment. */
r = MSK_makeenv(&env, NULL);
if (r == MSK_RES_OK)
{
/* Create the optimization task. */
r = MSK_maketask(env, 0, 0, &task);
if (r == MSK_RES_OK)
{
MSK_linkfunctotaskstream(task, MSK_STREAM_LOG, NULL, printstr);
/* Append empty constraints.
The constraints will initially have no bounds. */
if (r == MSK_RES_OK)
r = MSK_appendcons(task, numcon);
/* Append semidefinite variables. */
if (r == MSK_RES_OK)
r = MSK_appendbarvars(task, numbarvar, dimbarvar);
/* Set objective (6 nonzeros).*/
if (r == MSK_RES_OK)
r = MSK_putbarcblocktriplet(task, 6, Cj, Ck, Cl, Cv);
/* Set the equality constraint (6 nonzeros).*/
if (r == MSK_RES_OK)
r = MSK_putbarablocktriplet(task, 6, Ai, Aj, Ak, Al, Av);
/* Set the inequality constraint (1 nonzero).*/
if (r == MSK_RES_OK)
r = MSK_putbarablocktriplet(task, 1, &A2i, &A2j, &A2k, &A2l, &A2v);
/* Set constraint bounds */
if (r == MSK_RES_OK)
r = MSK_putconboundslice(task, 0, 2, bkc, blc, buc);
if (r == MSK_RES_OK)
{
MSKrescodee trmcode;
/* Run optimizer */
r = MSK_optimizetrm(task, &trmcode);
MSK_solutionsummary(task, MSK_STREAM_MSG);
if (r == MSK_RES_OK)
{
MSKsolstae solsta;
MSK_getsolsta(task, MSK_SOL_ITR, &solsta);
switch (solsta)
{
case MSK_SOL_STA_OPTIMAL:
/* Retrieve the soution for all symmetric variables */
printf("Solution (lower triangular part vectorized):\n");
for(i = 0; i < numbarvar; i++) {
dim = dimbarvar[i] * (dimbarvar[i] + 1) / 2;
barx = (MSKrealt *) MSK_calloctask(task, dim, sizeof(MSKrealt));
MSK_getbarxj(task, MSK_SOL_ITR, i, barx);
printf("X%d: ", i + 1);
for (j = 0; j < dim; ++j)
printf("%.3f ", barx[j]);
printf("\n");
MSK_freetask(task, barx);
}
break;
case MSK_SOL_STA_DUAL_INFEAS_CER:
case MSK_SOL_STA_PRIM_INFEAS_CER:
printf("Primal or dual infeasibility certificate found.\n");
break;
case MSK_SOL_STA_UNKNOWN:
printf("The status of the solution could not be determined. Termination code: %d.\n", trmcode);
break;
default:
printf("Other solution status.");
break;
}
}
else
{
printf("Error while optimizing.\n");
}
}
if (r != MSK_RES_OK)
{
/* In case of an error print error code and description. */
char symname[MSK_MAX_STR_LEN];
char desc[MSK_MAX_STR_LEN];
printf("An error occurred while optimizing.\n");
MSK_getcodedesc(r,
symname,
desc);
printf("Error %s - '%s'\n", symname, desc);
}
}
/* Delete the task and the associated data. */
MSK_deletetask(&task);
}
/* Delete the environment and the associated data. */
MSK_deleteenv(&env);
return (r);
} /* main */
sdo_lmi.c
/*
Copyright : Copyright (c) MOSEK ApS, Denmark. All rights reserved.
File : sdo_lmi.c
Purpose : To solve a problem with an LMI and an affine conic constrained problem with a PSD term
minimize Tr [1, 0; 0, 1]*X + x(1) + x(2) + 1
subject to Tr [0, 1; 1, 0]*X - x(1) - x(2) >= 0
x(1) [0, 1; 1, 3] + x(2) [3, 1; 1, 0] - [1, 0; 0, 1] >> 0
X >> 0
*/
#include <stdio.h>
#include <math.h>
#include "mosek.h" /* Include the MOSEK definition file. */
#define NUMVAR 2 /* Number of scalar variables */
#define NUMAFE 4 /* Number of affine expressions */
#define NUMFNZ 6 /* Number of non-zeros in F */
#define NUMBARVAR 1 /* Number of semidefinite variables */
static void MSKAPI printstr(void *handle,
const char str[])
{
printf("%s", str);
} /* printstr */
int main(int argc, const char *argv[])
{
MSKrescodee r;
const MSKint32t DIMBARVAR[] = {2}; /* Dimension of semidefinite cone */
MSKint64t LENBARVAR[] = {2 * (2 + 1) / 2}; /* Number of scalar SD variables */
const MSKint32t barc_j[] = {0, 0},
barc_k[] = {0, 1},
barc_l[] = {0, 1};
const MSKrealt barc_v[] = {1, 1};
const MSKint64t barf_i[] = {0,0};
const MSKint32t barf_j[] = {0,0},
barf_k[] = {0,1},
barf_l[] = {0,0};
const MSKrealt barf_v[] = {0,1};
const MSKint64t afeidx[] = {0, 0, 1, 2, 2, 3};
const MSKint32t varidx[] = {0, 1, 1, 0, 1, 0};
const MSKrealt f_val[] = {-1, -1, 3, sqrt(2), sqrt(2), 3},
g[] = {0, -1, 0, -1};
MSKrealt *xx, *barx;
MSKint32t i, j;
MSKenv_t env = NULL;
MSKtask_t task = NULL;
/* Create the mosek environment. */
r = MSK_makeenv(&env, NULL);
if (r == MSK_RES_OK)
{
/* Create the optimization task. */
r = MSK_maketask(env, 0, 0, &task);
if (r == MSK_RES_OK)
{
r = MSK_linkfunctotaskstream(task, MSK_STREAM_LOG, NULL, printstr);
/* Append 'NUMAFE' empty affine expressions. */
if (r == MSK_RES_OK)
r = MSK_appendafes(task, NUMAFE);
/* Append 'NUMVAR' scalar variables.
The variables will initially be fixed at zero (x=0). */
if (r == MSK_RES_OK)
r = MSK_appendvars(task, NUMVAR);
/* Append 'NUMBARVAR' semidefinite variables. */
if (r == MSK_RES_OK)
{
r = MSK_appendbarvars(task, NUMBARVAR, DIMBARVAR);
}
/* Set the constant term in the objective. */
if (r == MSK_RES_OK)
r = MSK_putcfix(task, 1.0);
/* Set c_j and the bounds for each scalar variable*/
for (j = 0; j < NUMVAR && r == MSK_RES_OK; ++j)
{
r = MSK_putcj(task, j, 1.0);
if (r==MSK_RES_OK)
r = MSK_putvarbound(task, j, MSK_BK_FR, -MSK_INFINITY, MSK_INFINITY);
}
/* Set the linear term barc_j in the objective.*/
if (r == MSK_RES_OK)
r = MSK_putbarcblocktriplet(task,
2,
barc_j,
barc_k,
barc_l,
barc_v);
/* Set the F matrix */
if (r == MSK_RES_OK)
r = MSK_putafefentrylist(task, NUMFNZ, afeidx, varidx, f_val);
/* Set the g vector */
if (r == MSK_RES_OK)
r = MSK_putafegslice(task, 0, NUMAFE, g);
/* Set the barF matrix */
if (r == MSK_RES_OK)
r = MSK_putafebarfblocktriplet(task,
2,
barf_i,
barf_j,
barf_k,
barf_l,
barf_v);
/* Append R+ domain and the corresponding ACC */
MSKint64t acc1_afeidx[] = {0};
if (r == MSK_RES_OK)
r = MSK_appendrplusdomain(task, 1, NULL);
if (r == MSK_RES_OK)
r = MSK_appendacc(task, 0, 1, acc1_afeidx, NULL);
/* Append the SVEC_PSD domain and the corresponding ACC */
MSKint64t acc2_afeidx[] = {1, 2, 3};
if (r == MSK_RES_OK)
r = MSK_appendsvecpsdconedomain(task, 3, NULL);
if (r == MSK_RES_OK)
r = MSK_appendacc(task, 1, 3, acc2_afeidx, NULL);
if (r == MSK_RES_OK)
{
MSKrescodee trmcode;
/* Run optimizer */
r = MSK_optimizetrm(task, &trmcode);
/* Print a summary containing information
about the solution for debugging purposes*/
MSK_solutionsummary(task, MSK_STREAM_MSG);
if (r == MSK_RES_OK)
{
MSKsolstae solsta;
MSK_getsolsta(task, MSK_SOL_ITR, &solsta);
switch (solsta)
{
case MSK_SOL_STA_OPTIMAL:
xx = (MSKrealt *) MSK_calloctask(task, NUMVAR, sizeof(MSKrealt));
barx = (MSKrealt *) MSK_calloctask(task, LENBARVAR[0], sizeof(MSKrealt));
MSK_getxx(task,MSK_SOL_ITR,xx);
MSK_getbarxj(task, MSK_SOL_ITR, 0, barx);
printf("Optimal primal solution\n");
for (i = 0; i < NUMVAR; ++i)
printf("x[%d] : % e\n", i, xx[i]);
for (i = 0; i < LENBARVAR[0]; ++i)
printf("barx[%d]: % e\n", i, barx[i]);
MSK_freetask(task, xx);
MSK_freetask(task, barx);
break;
case MSK_SOL_STA_DUAL_INFEAS_CER:
case MSK_SOL_STA_PRIM_INFEAS_CER:
printf("Primal or dual infeasibility certificate found.\n");
break;
case MSK_SOL_STA_UNKNOWN:
printf("The status of the solution could not be determined. Termination code: %d.\n", trmcode);
break;
default:
printf("Other solution status.");
break;
}
}
else
printf("Error while optimizing.\n");
}
if (r != MSK_RES_OK)
{
/* In case of an error print error code and description. */
char symname[MSK_MAX_STR_LEN];
char desc[MSK_MAX_STR_LEN];
printf("An error occurred while optimizing.\n");
MSK_getcodedesc(r, symname, desc);
printf("Error %s - '%s'\n", symname, desc);
}
}
/* Delete the task and the associated data. */
MSK_deletetask(&task);
}
/* Delete the environment and the associated data. */
MSK_deleteenv(&env);
return (r);
} /* main */
sensitivity.c
/*
Copyright: Copyright (c) MOSEK ApS, Denmark. All rights reserved.
File: sensitivity.c
Purpose: To demonstrate how to perform sensitivity
analysis from the API on a small problem:
minimize
obj: +1 x11 + 2 x12 + 5 x23 + 2 x24 + 1 x31 + 2 x33 + 1 x34
st
c1: + x11 + x12 <= 400
c2: + x23 + x24 <= 1200
c3: + x31 + x33 + x34 <= 1000
c4: + x11 + x31 = 800
c5: + x12 = 100
c6: + x23 + x33 = 500
c7: + x24 + x34 = 500
The example uses basis type sensitivity analysis.
*/
#include <stdio.h>
#include "mosek.h" /* Include the MOSEK definition file. */
static void MSKAPI printstr(void *handle,
const char str[])
{
printf("%s", str);
} /* printstr */
int main(int argc, char *argv[])
{
const MSKint32t numcon = 7,
numvar = 7;
MSKint32t i, j;
MSKboundkeye bkc[] = {MSK_BK_UP, MSK_BK_UP, MSK_BK_UP, MSK_BK_FX,
MSK_BK_FX, MSK_BK_FX, MSK_BK_FX
};
MSKboundkeye bkx[] = {MSK_BK_LO, MSK_BK_LO, MSK_BK_LO,
MSK_BK_LO, MSK_BK_LO, MSK_BK_LO, MSK_BK_LO
};
MSKint32t ptrb[] = {0, 2, 4, 6, 8, 10, 12};
MSKint32t ptre[] = {2, 4, 6, 8, 10, 12, 14};
MSKint32t sub[] = {0, 3, 0, 4, 1, 5, 1, 6, 2, 3, 2, 5, 2, 6};
MSKrealt blc[] = { -MSK_INFINITY, -MSK_INFINITY, -MSK_INFINITY, 800, 100, 500, 500};
MSKrealt buc[] = {400, 1200, 1000, 800, 100, 500, 500};
MSKrealt c[] = {1.0, 2.0, 5.0, 2.0, 1.0, 2.0, 1.0};
MSKrealt blx[] = {0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0};
MSKrealt bux[] = {MSK_INFINITY, MSK_INFINITY, MSK_INFINITY, MSK_INFINITY,
MSK_INFINITY, MSK_INFINITY, MSK_INFINITY
};
MSKrealt val[] = {1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0};
MSKrescodee r;
MSKenv_t env;
MSKtask_t task;
/* Create mosek environment. */
r = MSK_makeenv(&env, NULL);
if (r == MSK_RES_OK)
{
/* Make the optimization task. */
r = MSK_makeemptytask(env, &task);
if (r == MSK_RES_OK)
{
/* Directs the log task stream to the user
specified procedure 'printstr'. */
MSK_linkfunctotaskstream(task, MSK_STREAM_LOG, NULL, printstr);
MSK_echotask(task,
MSK_STREAM_MSG,
"Defining the problem data.\n");
}
/* Append the constraints. */
if (r == MSK_RES_OK)
r = MSK_appendcons(task, numcon);
/* Append the variables. */
if (r == MSK_RES_OK)
r = MSK_appendvars(task, numvar);
/* Put C. */
if (r == MSK_RES_OK)
r = MSK_putcfix(task, 0.0);
if (r == MSK_RES_OK)
r = MSK_putcslice(task, 0, numvar, c);
/* Put constraint bounds. */
if (r == MSK_RES_OK)
r = MSK_putconboundslice(task, 0, numcon, bkc, blc, buc);
/* Put variable bounds. */
if (r == MSK_RES_OK)
r = MSK_putvarboundslice(task, 0, numvar, bkx, blx, bux);
/* Put A. */
if (r == MSK_RES_OK)
r = MSK_putacolslice(task, 0, numvar, ptrb, ptre, sub, val);
if (r == MSK_RES_OK)
r = MSK_putobjsense(task, MSK_OBJECTIVE_SENSE_MINIMIZE);
if (r == MSK_RES_OK)
r = MSK_optimizetrm(task, NULL);
if (r == MSK_RES_OK)
{
/* Analyze upper bound on c1 and the equality constraint on c4 */
MSKint32t subi[] = {0, 3};
MSKmarke marki[] = {MSK_MARK_UP, MSK_MARK_UP};
/* Analyze lower bound on the variables x12 and x31 */
MSKint32t subj[] = {1, 4};
MSKmarke markj[] = {MSK_MARK_LO, MSK_MARK_LO};
MSKrealt leftpricei[2];
MSKrealt rightpricei[2];
MSKrealt leftrangei[2];
MSKrealt rightrangei[2];
MSKrealt leftpricej[2];
MSKrealt rightpricej[2];
MSKrealt leftrangej[2];
MSKrealt rightrangej[2];
r = MSK_primalsensitivity(task,
2,
subi,
marki,
2,
subj,
markj,
leftpricei,
rightpricei,
leftrangei,
rightrangei,
leftpricej,
rightpricej,
leftrangej,
rightrangej);
printf("Results from sensitivity analysis on bounds:\n");
printf("For constraints:\n");
for (i = 0; i < 2; ++i)
printf("leftprice = %e, rightprice = %e,leftrange = %e, rightrange =%e\n",
leftpricei[i], rightpricei[i], leftrangei[i], rightrangei[i]);
printf("For variables:\n");
for (i = 0; i < 2; ++i)
printf("leftprice = %e, rightprice = %e,leftrange = %e, rightrange =%e\n",
leftpricej[i], rightpricej[i], leftrangej[i], rightrangej[i]);
}
if (r == MSK_RES_OK)
{
MSKint32t subj[] = {2, 5};
MSKrealt leftprice[2];
MSKrealt rightprice[2];
MSKrealt leftrange[2];
MSKrealt rightrange[2];
r = MSK_dualsensitivity(task,
2,
subj,
leftprice,
rightprice,
leftrange,
rightrange
);
printf("Results from sensitivity analysis on objective coefficients:\n");
for (i = 0; i < 2; ++i)
printf("leftprice = %e, rightprice = %e,leftrange = %e, rightrange =%e\n",
leftprice[i], rightprice[i], leftrange[i], rightrange[i]);
}
MSK_deletetask(&task);
}
MSK_deleteenv(&env);
printf("Return code: %d (0 means no error occured.)\n", r);
return (r);
} /* main */
simple.c
/*
Copyright: Copyright (c) MOSEK ApS, Denmark. All rights reserved.
File: simple.c
Purpose: To demonstrate a very simple example using MOSEK by
reading a problem file, solving the problem and
writing the solution to a file.
*/
#include "mosek.h"
static void MSKAPI printstr(void *handle, const char str[])
{
printf("%s", str);
}
int main(int argc, const char * argv[])
{
MSKenv_t env = NULL;
MSKtask_t task = NULL;
MSKrescodee res = MSK_RES_OK, trmcode;
if (argc <= 1)
{
printf("Missing argument, syntax is:\n");
printf(" simple inputfile [ solutionfile ]\n");
}
else
{
// Create the mosek environment.
// The `NULL' arguments here, are used to specify customized
// memory allocators and a memory debug file. These can
// safely be ignored for now.
res = MSK_makeenv(&env, NULL);
// Create a task object linked with the environment env.
// We create it with 0 variables and 0 constraints initially,
// since we do not know the size of the problem.
if (res == MSK_RES_OK)
res = MSK_maketask(env, 0, 0, &task);
// Direct the task log stream to a user specified function
if (res == MSK_RES_OK)
res = MSK_linkfunctotaskstream(task, MSK_STREAM_LOG, NULL, printstr);
// We assume that a problem file was given as the first command
// line argument (received in `argv')
if (res == MSK_RES_OK)
res = MSK_readdata(task, argv[1]);
// Solve the problem
if (res == MSK_RES_OK)
res = MSK_optimizetrm(task, &trmcode);
// Print a summary of the solution.
if (res == MSK_RES_OK)
res = MSK_solutionsummary(task, MSK_STREAM_LOG);
// If an output file was specified, save problem to file
if (res == MSK_RES_OK && argc >= 3)
{
// If using OPF format, these parameters will specify what to include in output
MSK_putintparam(task, MSK_IPAR_OPF_WRITE_PROBLEM, MSK_ON);
MSK_putintparam(task, MSK_IPAR_OPF_WRITE_SOLUTIONS, MSK_ON);
MSK_putintparam(task, MSK_IPAR_OPF_WRITE_HINTS, MSK_OFF);
MSK_putintparam(task, MSK_IPAR_OPF_WRITE_PARAMETERS, MSK_OFF);
res = MSK_writedata(task, argv[2]);
}
// Delete task and environment
MSK_deletetask(&task);
MSK_deleteenv(&env);
}
return res;
}
solutionquality.c
/*
Copyright: Copyright (c) MOSEK ApS, Denmark. All rights reserved.
File: solutionquality.c
Purpose: To demonstrate how to examine the quality of a solution.
*/
#include <math.h>
#include "mosek.h"
static double dmin(double x,
double y)
{
return (x <= y) ? (x) : (y);
} /* dmin */
static double dmax(double x,
double y)
{
return (x >= y) ? (x) : (y);
} /* dmax */
static void MSKAPI printstr(void *handle,
const char str[])
{
printf("%s", str);
} /* printstr */
int main(int argc, const char * argv[])
{
double max_primal_viol, /* maximal primal violation */
max_dual_viol, /* maximal dual violation */
abs_obj_gap,
rel_obj_gap;
MSKenv_t env = NULL;
MSKint32t numvar, j;
MSKsolstae solsta;
MSKsoltypee whichsol = MSK_SOL_BAS;
MSKrealt primalobj, pviolcon, pviolvar, pviolbarvar, pviolcones, pviolitg,
dualobj, dviolcon, dviolvar, dviolbarvar, dviolcones, xj;
MSKrescodee r = MSK_RES_OK;
MSKrescodee trmcode;
MSKtask_t task = NULL;
int accepted = 0;
if (argc <= 1)
{
printf("Missing argument. The syntax is:\n");
printf(" solutionquality inputfile\n");
}
else
{
r = MSK_makeenv(&env, NULL);
if (r == MSK_RES_OK)
r = MSK_makeemptytask(env, &task);
if (r == MSK_RES_OK)
MSK_linkfunctotaskstream(task, MSK_STREAM_LOG, NULL, printstr);
/* We assume that a problem file was given as the first command
line argument (received in `argv'). */
if (r == MSK_RES_OK)
r = MSK_readdata(task, argv[1]);
/* Solve the problem */
if (r == MSK_RES_OK)
{
r = MSK_optimizetrm(task, &trmcode);
}
/* Print a summary of the solution. */
MSK_solutionsummary(task, MSK_STREAM_MSG);
if (r == MSK_RES_OK)
{
MSK_getsolsta(task, whichsol, &solsta);
r = MSK_getsolutioninfo(task,
whichsol,
&primalobj,
&pviolcon,
&pviolvar,
&pviolbarvar,
&pviolcones,
&pviolitg,
&dualobj,
&dviolcon,
&dviolvar,
&dviolbarvar,
&dviolcones);
switch (solsta)
{
case MSK_SOL_STA_OPTIMAL:
{
abs_obj_gap = fabs(dualobj - primalobj);
rel_obj_gap = abs_obj_gap / (1.0 + dmin(fabs(primalobj), fabs(dualobj)));
max_primal_viol = dmax(pviolcon, pviolvar);
max_primal_viol = dmax(max_primal_viol, pviolbarvar);
max_primal_viol = dmax(max_primal_viol, pviolcones);
max_dual_viol = dmax(dviolcon, dviolvar);
max_dual_viol = dmax(max_dual_viol, dviolbarvar);
max_dual_viol = dmax(max_dual_viol, dviolcones);
/* Assume the application needs the solution to be within
1e-6 optimality in an absolute sense. Another approach
would be looking at the relative objective gap */
printf("\n\n");
printf("Customized solution information.\n");
printf(" Absolute objective gap: %e\n", abs_obj_gap);
printf(" Relative objective gap: %e\n", rel_obj_gap);
printf(" Max primal violation : %e\n", max_primal_viol);
printf(" Max dual violation : %e\n", max_dual_viol);
if (rel_obj_gap > 1e-6)
{
printf("Warning: The relative objective gap is LARGE.\n");
accepted = 0;
}
/* We will accept a primal infeasibility of 1e-8 and
dual infeasibility of 1e-6. These number should chosen problem
dependent.
*/
if (max_primal_viol > 1e-8)
{
printf("Warning: Primal violation is too LARGE.\n");
accepted = 0;
}
if (max_dual_viol > 1e-6)
{
printf("Warning: Dual violation is too LARGE.\n");
accepted = 0;
}
if (accepted)
{
if (MSK_RES_OK == MSK_getnumvar(task, &numvar))
{
printf("Optimal primal solution\n");
for (j = 0; j < numvar && r == MSK_RES_OK; ++j)
{
r = MSK_getxxslice(task, whichsol, j, j + 1, &xj);
if (r == MSK_RES_OK)
printf("x[%d]: %e\n", j, xj);
}
}
}
else if (r == MSK_RES_OK)
{
/* Print detailed information about the solution */
r = MSK_analyzesolution(task, MSK_STREAM_LOG, whichsol);
}
break;
}
case MSK_SOL_STA_DUAL_INFEAS_CER:
case MSK_SOL_STA_PRIM_INFEAS_CER:
printf("Primal or dual infeasibility certificate found.\n");
break;
case MSK_SOL_STA_UNKNOWN:
printf("The status of the solution is unknown. Termination code: %d.\n", trmcode);
break;
default:
printf("Other solution status");
break;
}
}
MSK_deletetask(&task);
MSK_deleteenv(&env);
}
return (r);
}
solvebasis.c
/*
Copyright: Copyright (c) MOSEK ApS, Denmark. All rights reserved.
File: solvebasis.c
Purpose: To demonstrate the usage of
MSK_solvewithbasis on the problem:
maximize x0 + x1
st.
x0 + 2.0 x1 <= 2
x0 + x1 <= 6
x0 >= 0, x1>= 0
The problem has the slack variables
xc0, xc1 on the constraints
and the variables x0 and x1.
maximize x0 + x1
st.
x0 + 2.0 x1 -xc1 = 2
x0 + x1 -xc2 = 6
x0 >= 0, x1>= 0,
xc1 <= 0 , xc2 <= 0
Syntax: solvebasis
*/
#include "mosek.h"
static void MSKAPI printstr(void *handle,
const char str[])
{
printf("%s", str);
} /* printstr */
int main(int argc, const char *argv[])
{
MSKenv_t env;
MSKtask_t task;
MSKint32t numcon = 2, numvar = 2;
double c[] = {1.0, 1.0};
MSKint32t ptrb[] = {0, 2},
ptre[] = {2, 3};
MSKint32t asub[] = {0, 1, 0, 1};
double aval[] = {1.0, 1.0, 2.0, 1.0};
MSKboundkeye bkc[] = { MSK_BK_UP, MSK_BK_UP };
double blc[] = { -MSK_INFINITY, -MSK_INFINITY };
double buc[] = {2.0, 6.0};
MSKboundkeye bkx[] = { MSK_BK_LO, MSK_BK_LO };
double blx[] = {0.0, 0.0};
double bux[] = { +MSK_INFINITY, +MSK_INFINITY};
MSKrescodee r = MSK_RES_OK;
MSKint32t i, nz;
double w[] = {2.0, 6.0};
MSKint32t sub[] = {0, 1};
MSKint32t *basis;
if (r == MSK_RES_OK)
r = MSK_makeenv(&env, NULL);
if (r == MSK_RES_OK)
r = MSK_makeemptytask(env, &task);
if (r == MSK_RES_OK)
MSK_linkfunctotaskstream(task, MSK_STREAM_LOG, NULL, printstr);
if (r == MSK_RES_OK)
r = MSK_inputdata(task, numcon, numvar, numcon, numvar,
c, 0.0,
ptrb, ptre, asub, aval, bkc, blc, buc, bkx, blx, bux);
if (r == MSK_RES_OK)
r = MSK_putobjsense(task, MSK_OBJECTIVE_SENSE_MAXIMIZE);
if (r == MSK_RES_OK)
r = MSK_optimizetrm(task, NULL);
if (r == MSK_RES_OK)
basis = MSK_calloctask(task, numcon, sizeof(MSKint32t));
if (r == MSK_RES_OK)
r = MSK_initbasissolve(task, basis);
/* List basis variables corresponding to columns of B */
for (i = 0; i < numcon && r == MSK_RES_OK; ++i)
{
printf("basis[%d] = %d\n", i, basis[i]);
if (basis[sub[i]] < numcon)
printf("Basis variable no %d is xc%d.\n", i, basis[i]);
else
printf("Basis variable no %d is x%d.\n", i, basis[i] - numcon);
}
nz = 2;
/* solve Bx = w */
/* sub contains index of non-zeros in w.
On return w contains the solution x and sub
the index of the non-zeros in x.
*/
if (r == MSK_RES_OK)
r = MSK_solvewithbasis(task, 0, nz, sub, w, &nz);
if (r == MSK_RES_OK)
{
printf("\nSolution to Bx = w:\n\n");
/* Print solution and b. */
for (i = 0; i < nz; ++i)
{
if (basis[sub[i]] < numcon)
printf("xc%d = %e\n", basis[sub[i]] , w[sub[i]]);
else
printf("x%d = %e\n", basis[sub[i]] - numcon , w[sub[i]]);
}
}
/* Solve B^T y = w */
nz = 1; /* Only one element in sub is nonzero. */
sub[0] = 1; /* Only w[1] is nonzero. */
w[0] = 0.0;
w[1] = 1.0;
if (r == MSK_RES_OK)
r = MSK_solvewithbasis(task, 1, nz, sub, w, &nz);
if (r == MSK_RES_OK)
{
printf("\nSolution to B^T y = w:\n\n");
/* Print solution and y. */
for (i = 0; i < nz; ++i)
printf("y%d = %e\n", sub[i], w[sub[i]]);
}
return (r);
}/* main */
solvelinear.c
/*
Copyright: Copyright (c) MOSEK ApS, Denmark. All rights reserved.
File : solvelinear.c
Purpose : To demonstrate the usage of MSK_solvewithbasis
to solve the linear system:
1.0 x1 = b1
-1.0 x0 + 1.0 x1 = b2
with two different right hand sides
b = (1.0, -2.0)
and
b = (7.0, 0.0)
*/
#include "mosek.h"
static void MSKAPI printstr(void *handle,
const char str[])
{
printf("%s", str);
} /* printstr */
static MSKrescodee setup(MSKtask_t task,
double *aval,
MSKint32t *asub,
MSKint32t *ptrb,
MSKint32t *ptre,
MSKint32t numvar,
MSKint32t *basis)
{
MSKint32t i, j;
MSKrescodee r = MSK_RES_OK;
MSKstakeye *skx = NULL , *skc = NULL;
skx = (MSKstakeye *) calloc(numvar, sizeof(MSKstakeye));
if (skx == NULL && numvar)
r = MSK_RES_ERR_SPACE;
skc = (MSKstakeye *) calloc(numvar, sizeof(MSKstakeye));
if (skc == NULL && numvar)
r = MSK_RES_ERR_SPACE;
for (i = 0; i < numvar && r == MSK_RES_OK; ++i)
{
skx[i] = MSK_SK_BAS;
skc[i] = MSK_SK_FIX;
}
/* Create a coefficient matrix and right hand
side with the data from the linear system */
if (r == MSK_RES_OK)
r = MSK_appendvars(task, numvar);
if (r == MSK_RES_OK)
r = MSK_appendcons(task, numvar);
for (i = 0; i < numvar && r == MSK_RES_OK; ++i)
r = MSK_putacol(task, i, ptre[i] - ptrb[i], asub + ptrb[i], aval + ptrb[i]);
for (i = 0; i < numvar && r == MSK_RES_OK; ++i)
r = MSK_putconbound(task, i, MSK_BK_FX, 0, 0);
for (i = 0; i < numvar && r == MSK_RES_OK; ++i)
r = MSK_putvarbound(task, i, MSK_BK_FR, -MSK_INFINITY, MSK_INFINITY);
/* Allocate space for the solution and set status to unknown */
if (r == MSK_RES_OK)
r = MSK_deletesolution(task, MSK_SOL_BAS);
/* Setup status keys. That is all that is needed. */
if (r == MSK_RES_OK)
r = MSK_putskcslice(task, MSK_SOL_BAS, 0, numvar, skc);
if (r == MSK_RES_OK)
r = MSK_putskxslice(task, MSK_SOL_BAS, 0, numvar, skx);
if (r == MSK_RES_OK)
r = MSK_initbasissolve(task, basis);
free(skx);
free(skc);
return (r);
}
#define NUMCON 2
#define NUMVAR 2
int main(int argc, const char *argv[])
{
MSKint32t numvar = NUMCON,
numcon = NUMVAR; /* we must have numvar == numcon */
MSKenv_t env;
MSKtask_t task;
MSKrescodee r = MSK_RES_OK;
MSKint32t i, nz;
double aval[] = { -1.0, 1.0, 1.0};
MSKint32t asub[] = {1, 0, 1};
MSKint32t ptrb[] = {0, 1};
MSKint32t ptre[] = {1, 3};
MSKint32t bsub[NUMCON];
double b[NUMCON];
MSKint32t *basis = NULL;
if (r == MSK_RES_OK)
r = MSK_makeenv(&env, NULL);
if (r == MSK_RES_OK)
r = MSK_makeemptytask(env, &task);
if (r == MSK_RES_OK)
MSK_linkfunctotaskstream(task, MSK_STREAM_LOG, NULL, printstr);
basis = (MSKint32t *) calloc(numcon, sizeof(MSKint32t));
if (basis == NULL && numvar)
r = MSK_RES_ERR_SPACE;
/* setup: Put A matrix and factor A.
Call this function only once for a given task. */
if (r == MSK_RES_OK)
r = setup(task,
aval,
asub,
ptrb,
ptre,
numvar,
basis
);
/* now solve rhs */
b[0] = 1;
b[1] = -2;
bsub[0] = 0;
bsub[1] = 1;
nz = 2;
if (r == MSK_RES_OK)
r = MSK_solvewithbasis(task, 0, nz, bsub, b, &nz);
if (r == MSK_RES_OK)
{
printf("\nSolution to Bx = b:\n\n");
/* Print solution and show correspondents
to original variables in the problem */
for (i = 0; i < nz; ++i)
{
if (basis[bsub[i]] < numcon)
printf("This should never happen\n");
else
printf("x%d = %e\n", basis[bsub[i]] - numcon , b[bsub[i]]);
}
}
b[0] = 7;
bsub[0] = 0;
nz = 1;
if (r == MSK_RES_OK)
r = MSK_solvewithbasis(task, 0, nz, bsub, b, &nz);
if (r == MSK_RES_OK)
{
printf("\nSolution to Bx = b:\n\n");
/* Print solution and show correspondents
to original variables in the problem */
for (i = 0; i < nz; ++i)
{
if (basis[bsub[i]] < numcon)
printf("This should never happen\n");
else
printf("x%d = %e\n", basis[bsub[i]] - numcon , b[bsub[i]]);
}
}
free(basis);
return r;
}
sparsecholesky.c
/*
Copyright: Copyright (c) MOSEK ApS, Denmark. All rights reserved.
File: sparsecholesky.c
Purpose: Demonstrate the sparse Cholesky factorization.
*/
#include <stdio.h>
#include "mosek.h"
/* Prints out a Cholesky factor presented in sparse form */
static void printsparse(MSKint32t n,
MSKint32t *perm,
MSKrealt *diag,
MSKint32t *lnzc,
MSKint64t *lptrc,
MSKint64t lensubnval,
MSKint32t *lsubc,
MSKrealt *lvalc)
{
int i, j;
MSKrealt*l;
printf("P = [ ");
for (i = 0; i < n; i++) printf("%d ", perm[i]);
printf("]\ndiag(D) = [ ");
for (i = 0; i < n; i++) printf("%.2e ", diag[i]);
printf("]\nL=\n");
l = (MSKrealt*) calloc(n * n, sizeof(MSKrealt));
for (j = 0; j < n; j++)
for (i = lptrc[j]; i < lptrc[j] + lnzc[j]; i++)
l[lsubc[i]*n + j] = lvalc[i];
for (i = 0; i < n; i++) {
for (j = 0; j < n; j++) printf("%.2e ", l[n * i + j]);
printf("\n");
}
free(l);
}
int main(int argc, const char *argv[])
{
MSKenv_t env;
MSKrescodee r;
/* The "" makes leak detection possible at a small cost.
Otherwise use NULL instead of "". */
r = MSK_makeenv(&env, "");
if (r == MSK_RES_OK)
{
const MSKint32t n = 4; // Data from the example in the text
//Observe that anzc, aptrc, asubc and avalc only specify the lower triangular part.
const MSKint32t anzc[] = {4, 1, 1, 1},
asubc[] = {0, 1, 2, 3, 1, 2, 3};
const MSKint64t aptrc[] = {0, 4, 5, 6};
const MSKrealt avalc[] = {4.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0},
b[] = {13.0, 3.0, 4.0, 5.0};
MSKint32t *perm = NULL, *lnzc = NULL, *lsubc = NULL;
MSKint64t lensubnval, *lptrc = NULL;
MSKrealt *diag = NULL, *lvalc = NULL;
printf("\nExample with positive definite A.\n");
r = MSK_computesparsecholesky(env,
0, /* Mosek chooses number of threads */
1, /* Apply a reordering heuristic */
1.0e-14, /* Singularity tolerance */
n, anzc, aptrc, asubc, avalc,
&perm, &diag, &lnzc, &lptrc, &lensubnval, &lsubc, &lvalc);
if (r == MSK_RES_OK)
{
MSKint32t i, j;
MSKrealt *x;
printsparse(n, perm, diag, lnzc, lptrc, lensubnval, lsubc, lvalc);
x = MSK_callocenv(env, n, sizeof(MSKrealt));
if (x)
{
/* Permuted b is stored as x. */
for (i = 0; i < n; ++i) x[i] = b[perm[i]];
/* Compute inv(L)*x. */
r = MSK_sparsetriangularsolvedense(env, MSK_TRANSPOSE_NO, n,
lnzc, lptrc, lensubnval, lsubc, lvalc, x);
if (r == MSK_RES_OK) {
/* Compute inv(L^T)*x. */
r = MSK_sparsetriangularsolvedense(env, MSK_TRANSPOSE_YES, n,
lnzc, lptrc, lensubnval, lsubc, lvalc, x);
printf("\nSolution A x = b, x = [ ");
for (i = 0; i < n; i++)
for (j = 0; j < n; j++) if (perm[j] == i) printf("%.2f ", x[j]);
printf("]\n");
}
MSK_freeenv(env, x);
}
else
printf("Out of space while creating x.\n");
}
else
printf("Cholesky computation failed: %d\n", (int) r);
MSK_freeenv(env, perm);
MSK_freeenv(env, lnzc);
MSK_freeenv(env, lsubc);
MSK_freeenv(env, lptrc);
MSK_freeenv(env, diag);
MSK_freeenv(env, lvalc);
}
if (r == MSK_RES_OK)
{
const MSKint32t n = 3;
const MSKint32t anzc[] = {3, 2, 1},
asubc[] = {0, 1, 2, 1, 2, 2};
const MSKint64t aptrc[] = {0, 3, 5};
const MSKrealt avalc[] = {1.0, 1.0, 1.0, 1.0, 1.0, 1.0};
MSKint32t *perm = NULL, *lnzc = NULL, *lsubc = NULL;
MSKint64t lensubnval, *lptrc = NULL;
MSKrealt *diag = NULL, *lvalc = NULL;
/* Let A be
[1.0 1.0 1.0]
[1.0 1.0 1.0]
[1.0 1.0 1.0]
then compute a sparse Cholesky factorization A. Observe A is NOT
positive definite.
*/
printf("\nExample with a semidefinite A.\n");
r = MSK_computesparsecholesky(env,
0, /* Mosek chooses number of threads */
1, /* Use reordering heuristic */
1.0e-14, /* Singularity tolerance */
n, anzc, aptrc, asubc, avalc,
&perm, &diag, &lnzc, &lptrc, &lensubnval, &lsubc, &lvalc);
if (r == MSK_RES_OK)
printsparse(n, perm, diag, lnzc, lptrc, lensubnval, lsubc, lvalc);
MSK_freeenv(env, perm);
MSK_freeenv(env, diag);
MSK_freeenv(env, lnzc);
MSK_freeenv(env, lptrc);
MSK_freeenv(env, lsubc);
MSK_freeenv(env, lvalc);
}
if (r == MSK_RES_OK)
r = MSK_deleteenv(&env); /* Catch leaks */
else
MSK_deleteenv(&env);
return (r);
} /* main */
unicode.c
/*
Copyright: Copyright (c) MOSEK ApS, Denmark. All rights reserved.
File: unicode.c
Purpose: To demonstrate how to use unicoded strings.
*/
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include "mosek.h"
int main(int argc, const char *argv[])
{
char output[512];
wchar_t *input = L"My task name";
MSKenv_t env;
MSKrescodee r;
MSKtask_t task;
size_t len, conv;
r = MSK_makeenv(&env, NULL);
if (r == MSK_RES_OK)
{
r = MSK_makeemptytask(env, &task);
if (r == MSK_RES_OK)
{
/*
The wchar_t string input specifying the task name
is converted to a UTF8 string that can be inputted
to MOSEK.
*/
r = MSK_wchartoutf8(sizeof(output), &len, &conv, output, input);
if (r == MSK_RES_OK)
r = MSK_puttaskname(task, output);
MSK_deletetask(&task);
}
MSK_deleteenv(&env);
}
printf("Return code - %d\n", r);
return (r);
} /* main */
