/* 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 #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 */