10.4 Constants

10.4.1 Basis identification

MSK_BI_NEVER

Never do basis identification.

MSK_BI_ALWAYS

Basis identification is always performed even if the interior-point optimizer terminates abnormally.

MSK_BI_NO_ERROR

Basis identification is performed if the interior-point optimizer terminates without an error.

MSK_BI_IF_FEASIBLE

Basis identification is not performed if the interior-point optimizer terminates with a problem status saying that the problem is primal or dual infeasible.

MSK_BI_RESERVERED

Not currently in use.

10.4.2 Bound keys

MSK_BK_LO

The constraint or variable has a finite lower bound and an infinite upper bound.

MSK_BK_UP

The constraint or variable has an infinite lower bound and an finite upper bound.

MSK_BK_FX

The constraint or variable is fixed.

MSK_BK_FR

The constraint or variable is free.

MSK_BK_RA

The constraint or variable is ranged.

10.4.3 Mark

MSK_MARK_LO

The lower bound is selected for sensitivity analysis.

MSK_MARK_UP

The upper bound is selected for sensitivity analysis.

10.4.4 TBD

MSK_SIM_PRECISION_NORMAL

TBD

MSK_SIM_PRECISION_EXTENDED

TBD

10.4.5 Degeneracy strategies

MSK_SIM_DEGEN_NONE

The simplex optimizer should use no degeneration strategy.

MSK_SIM_DEGEN_FREE

The simplex optimizer chooses the degeneration strategy.

MSK_SIM_DEGEN_AGGRESSIVE

The simplex optimizer should use an aggressive degeneration strategy.

MSK_SIM_DEGEN_MODERATE

The simplex optimizer should use a moderate degeneration strategy.

MSK_SIM_DEGEN_MINIMUM

The simplex optimizer should use a minimum degeneration strategy.

10.4.6 Transposed matrix.

MSK_TRANSPOSE_NO

No transpose is applied.

MSK_TRANSPOSE_YES

A transpose is applied.

10.4.7 Triangular part of a symmetric matrix.

MSK_UPLO_LO

Lower part.

MSK_UPLO_UP

Upper part.

10.4.8 Problem reformulation.

MSK_SIM_REFORMULATION_ON

Allow the simplex optimizer to reformulate the problem.

MSK_SIM_REFORMULATION_OFF

Disallow the simplex optimizer to reformulate the problem.

MSK_SIM_REFORMULATION_FREE

The simplex optimizer can choose freely.

MSK_SIM_REFORMULATION_AGGRESSIVE

The simplex optimizer should use an aggressive reformulation strategy.

10.4.9 Exploit duplicate columns.

MSK_SIM_EXPLOIT_DUPVEC_ON

Allow the simplex optimizer to exploit duplicated columns.

MSK_SIM_EXPLOIT_DUPVEC_OFF

Disallow the simplex optimizer to exploit duplicated columns.

MSK_SIM_EXPLOIT_DUPVEC_FREE

The simplex optimizer can choose freely.

10.4.10 Hot-start type employed by the simplex optimizer

MSK_SIM_HOTSTART_NONE

The simplex optimizer performs a coldstart.

MSK_SIM_HOTSTART_FREE

The simplex optimize chooses the hot-start type.

MSK_SIM_HOTSTART_STATUS_KEYS

Only the status keys of the constraints and variables are used to choose the type of hot-start.

10.4.11 Hot-start type employed by the interior-point optimizers.

MSK_INTPNT_HOTSTART_NONE

The interior-point optimizer performs a coldstart.

MSK_INTPNT_HOTSTART_PRIMAL

The interior-point optimizer exploits the primal solution only.

MSK_INTPNT_HOTSTART_DUAL

The interior-point optimizer exploits the dual solution only.

MSK_INTPNT_HOTSTART_PRIMAL_DUAL

The interior-point optimizer exploits both the primal and dual solution.

10.4.12 Solution purification employed optimizer.

MSK_PURIFY_NONE

The optimizer performs no solution purification.

MSK_PURIFY_PRIMAL

The optimizer purifies the primal solution.

MSK_PURIFY_DUAL

The optimizer purifies the dual solution.

MSK_PURIFY_PRIMAL_DUAL

The optimizer purifies both the primal and dual solution.

MSK_PURIFY_AUTO

TBD

10.4.13 Progress callback codes

MSK_CALLBACK_BEGIN_BI

The basis identification procedure has been started.

MSK_CALLBACK_BEGIN_CONIC

The callback function is called when the conic optimizer is started.

MSK_CALLBACK_BEGIN_DUAL_BI

The callback function is called from within the basis identification procedure when the dual phase is started.

MSK_CALLBACK_BEGIN_DUAL_SENSITIVITY

Dual sensitivity analysis is started.

MSK_CALLBACK_BEGIN_DUAL_SETUP_BI

The callback function is called when the dual BI phase is started.

MSK_CALLBACK_BEGIN_DUAL_SIMPLEX

The callback function is called when the dual simplex optimizer started.

MSK_CALLBACK_BEGIN_DUAL_SIMPLEX_BI

The callback function is called from within the basis identification procedure when the dual simplex clean-up phase is started.

MSK_CALLBACK_BEGIN_FOLDING

The calback function is called at the beginning of folding.

MSK_CALLBACK_BEGIN_FOLDING_BI

TBD

MSK_CALLBACK_BEGIN_FOLDING_BI_DUAL

TBD

MSK_CALLBACK_BEGIN_FOLDING_BI_INITIALIZE

TBD

MSK_CALLBACK_BEGIN_FOLDING_BI_OPTIMIZER

TBD

MSK_CALLBACK_BEGIN_FOLDING_BI_PRIMAL

TBD

MSK_CALLBACK_BEGIN_INFEAS_ANA

The callback function is called when the infeasibility analyzer is started.

MSK_CALLBACK_BEGIN_INITIALIZE_BI

The callback function is called from within the basis identification procedure when the initialization phase is started.

MSK_CALLBACK_BEGIN_INTPNT

The callback function is called when the interior-point optimizer is started.

MSK_CALLBACK_BEGIN_LICENSE_WAIT

Begin waiting for license.

MSK_CALLBACK_BEGIN_MIO

The callback function is called when the mixed-integer optimizer is started.

MSK_CALLBACK_BEGIN_OPTIMIZE_BI

TBD.

MSK_CALLBACK_BEGIN_OPTIMIZER

The callback function is called when the optimizer is started.

MSK_CALLBACK_BEGIN_PRESOLVE

The callback function is called when the presolve is started.

MSK_CALLBACK_BEGIN_PRIMAL_BI

The callback function is called from within the basis identification procedure when the primal phase is started.

MSK_CALLBACK_BEGIN_PRIMAL_REPAIR

Begin primal feasibility repair.

MSK_CALLBACK_BEGIN_PRIMAL_SENSITIVITY

Primal sensitivity analysis is started.

MSK_CALLBACK_BEGIN_PRIMAL_SETUP_BI

The callback function is called when the primal BI setup is started.

MSK_CALLBACK_BEGIN_PRIMAL_SIMPLEX

The callback function is called when the primal simplex optimizer is started.

MSK_CALLBACK_BEGIN_PRIMAL_SIMPLEX_BI

The callback function is called from within the basis identification procedure when the primal simplex clean-up phase is started.

MSK_CALLBACK_BEGIN_QCQO_REFORMULATE

Begin QCQO reformulation.

MSK_CALLBACK_BEGIN_READ

MOSEK has started reading a problem file.

MSK_CALLBACK_BEGIN_ROOT_CUTGEN

The callback function is called when root cut generation is started.

MSK_CALLBACK_BEGIN_SIMPLEX

The callback function is called when the simplex optimizer is started.

MSK_CALLBACK_BEGIN_SOLVE_ROOT_RELAX

The callback function is called when solution of root relaxation is started.

MSK_CALLBACK_BEGIN_TO_CONIC

Begin conic reformulation.

MSK_CALLBACK_BEGIN_WRITE

MOSEK has started writing a problem file.

MSK_CALLBACK_CONIC

The callback function is called from within the conic optimizer after the information database has been updated.

MSK_CALLBACK_DECOMP_MIO

The callback function is called when the dedicated algorithm for independent blocks inside the mixed-integer solver is started.

MSK_CALLBACK_DUAL_SIMPLEX

The callback function is called from within the dual simplex optimizer.

MSK_CALLBACK_END_BI

The callback function is called when the basis identification procedure is terminated.

MSK_CALLBACK_END_CONIC

The callback function is called when the conic optimizer is terminated.

MSK_CALLBACK_END_DUAL_BI

The callback function is called from within the basis identification procedure when the dual phase is terminated.

MSK_CALLBACK_END_DUAL_SENSITIVITY

Dual sensitivity analysis is terminated.

MSK_CALLBACK_END_DUAL_SETUP_BI

The callback function is called when the dual BI phase is terminated.

MSK_CALLBACK_END_DUAL_SIMPLEX

The callback function is called when the dual simplex optimizer is terminated.

MSK_CALLBACK_END_DUAL_SIMPLEX_BI

The callback function is called from within the basis identification procedure when the dual clean-up phase is terminated.

MSK_CALLBACK_END_FOLDING

The calback function is called at the end of folding.

MSK_CALLBACK_END_FOLDING_BI

TBD

MSK_CALLBACK_END_FOLDING_BI_DUAL

TBD

MSK_CALLBACK_END_FOLDING_BI_INITIALIZE

TBD

MSK_CALLBACK_END_FOLDING_BI_OPTIMIZER

TBD

MSK_CALLBACK_END_FOLDING_BI_PRIMAL

TBD

MSK_CALLBACK_END_INFEAS_ANA

The callback function is called when the infeasibility analyzer is terminated.

MSK_CALLBACK_END_INITIALIZE_BI

The callback function is called from within the basis identification procedure when the initialization phase is terminated.

MSK_CALLBACK_END_INTPNT

The callback function is called when the interior-point optimizer is terminated.

MSK_CALLBACK_END_LICENSE_WAIT

End waiting for license.

MSK_CALLBACK_END_MIO

The callback function is called when the mixed-integer optimizer is terminated.

MSK_CALLBACK_END_OPTIMIZE_BI

TBD.

MSK_CALLBACK_END_OPTIMIZER

The callback function is called when the optimizer is terminated.

MSK_CALLBACK_END_PRESOLVE

The callback function is called when the presolve is completed.

MSK_CALLBACK_END_PRIMAL_BI

The callback function is called from within the basis identification procedure when the primal phase is terminated.

MSK_CALLBACK_END_PRIMAL_REPAIR

End primal feasibility repair.

MSK_CALLBACK_END_PRIMAL_SENSITIVITY

Primal sensitivity analysis is terminated.

MSK_CALLBACK_END_PRIMAL_SETUP_BI

The callback function is called when the primal BI setup is terminated.

MSK_CALLBACK_END_PRIMAL_SIMPLEX

The callback function is called when the primal simplex optimizer is terminated.

MSK_CALLBACK_END_PRIMAL_SIMPLEX_BI

The callback function is called from within the basis identification procedure when the primal clean-up phase is terminated.

MSK_CALLBACK_END_QCQO_REFORMULATE

End QCQO reformulation.

MSK_CALLBACK_END_READ

MOSEK has finished reading a problem file.

MSK_CALLBACK_END_ROOT_CUTGEN

The callback function is called when root cut generation is terminated.

MSK_CALLBACK_END_SIMPLEX

The callback function is called when the simplex optimizer is terminated.

MSK_CALLBACK_END_SIMPLEX_BI

The callback function is called from within the basis identification procedure when the simplex clean-up phase is terminated.

MSK_CALLBACK_END_SOLVE_ROOT_RELAX

The callback function is called when solution of root relaxation is terminated.

MSK_CALLBACK_END_TO_CONIC

End conic reformulation.

MSK_CALLBACK_END_WRITE

MOSEK has finished writing a problem file.

MSK_CALLBACK_FOLDING_BI_DUAL

TBD

MSK_CALLBACK_FOLDING_BI_OPTIMIZER

TBD

MSK_CALLBACK_FOLDING_BI_PRIMAL

TBD

MSK_CALLBACK_HEARTBEAT

A heartbeat callback.

MSK_CALLBACK_IM_DUAL_SENSIVITY

The callback function is called at an intermediate stage of the dual sensitivity analysis.

MSK_CALLBACK_IM_DUAL_SIMPLEX

The callback function is called at an intermediate point in the dual simplex optimizer.

MSK_CALLBACK_IM_LICENSE_WAIT

MOSEK is waiting for a license.

MSK_CALLBACK_IM_LU

The callback function is called from within the LU factorization procedure at an intermediate point.

MSK_CALLBACK_IM_MIO

The callback function is called at an intermediate point in the mixed-integer optimizer.

MSK_CALLBACK_IM_MIO_DUAL_SIMPLEX

The callback function is called at an intermediate point in the mixed-integer optimizer while running the dual simplex optimizer.

MSK_CALLBACK_IM_MIO_INTPNT

The callback function is called at an intermediate point in the mixed-integer optimizer while running the interior-point optimizer.

MSK_CALLBACK_IM_MIO_PRIMAL_SIMPLEX

The callback function is called at an intermediate point in the mixed-integer optimizer while running the primal simplex optimizer.

MSK_CALLBACK_IM_ORDER

The callback function is called from within the matrix ordering procedure at an intermediate point.

MSK_CALLBACK_IM_PRIMAL_SENSIVITY

The callback function is called at an intermediate stage of the primal sensitivity analysis.

MSK_CALLBACK_IM_PRIMAL_SIMPLEX

The callback function is called at an intermediate point in the primal simplex optimizer.

MSK_CALLBACK_IM_READ

Intermediate stage in reading.

MSK_CALLBACK_IM_ROOT_CUTGEN

The callback is called from within root cut generation at an intermediate stage.

MSK_CALLBACK_IM_SIMPLEX

The callback function is called from within the simplex optimizer at an intermediate point.

MSK_CALLBACK_INTPNT

The callback function is called from within the interior-point optimizer after the information database has been updated.

MSK_CALLBACK_NEW_INT_MIO

The callback function is called after a new integer solution has been located by the mixed-integer optimizer.

MSK_CALLBACK_OPTIMIZE_BI

TBD.

MSK_CALLBACK_PRIMAL_SIMPLEX

The callback function is called from within the primal simplex optimizer.

MSK_CALLBACK_QO_REFORMULATE

The callback function is called at an intermediate stage of the conic quadratic reformulation.

MSK_CALLBACK_READ_OPF

The callback function is called from the OPF reader.

MSK_CALLBACK_READ_OPF_SECTION

A chunk of \(Q\) non-zeros has been read from a problem file.

MSK_CALLBACK_RESTART_MIO

The callback function is called when the mixed-integer optimizer is restarted.

MSK_CALLBACK_SOLVING_REMOTE

The callback function is called while the task is being solved on a remote server.

MSK_CALLBACK_UPDATE_DUAL_BI

The callback function is called from within the basis identification procedure at an intermediate point in the dual phase.

MSK_CALLBACK_UPDATE_DUAL_SIMPLEX

The callback function is called in the dual simplex optimizer.

MSK_CALLBACK_UPDATE_DUAL_SIMPLEX_BI

The callback function is called from within the basis identification procedure at an intermediate point in the dual simplex clean-up phase. The frequency of the callbacks is controlled by the MSK_IPAR_LOG_SIM_FREQ parameter.

MSK_CALLBACK_UPDATE_PRESOLVE

The callback function is called from within the presolve procedure.

MSK_CALLBACK_UPDATE_PRIMAL_BI

The callback function is called from within the basis identification procedure at an intermediate point in the primal phase.

MSK_CALLBACK_UPDATE_PRIMAL_SIMPLEX

The callback function is called in the primal simplex optimizer.

MSK_CALLBACK_UPDATE_PRIMAL_SIMPLEX_BI

The callback function is called from within the basis identification procedure at an intermediate point in the primal simplex clean-up phase. The frequency of the callbacks is controlled by the MSK_IPAR_LOG_SIM_FREQ parameter.

MSK_CALLBACK_UPDATE_SIMPLEX

The callback function is called from simplex optimizer.

MSK_CALLBACK_WRITE_OPF

The callback function is called from the OPF writer.

10.4.14 Compression types

MSK_COMPRESS_NONE

No compression is used.

MSK_COMPRESS_FREE

The type of compression used is chosen automatically.

MSK_COMPRESS_GZIP

The type of compression used is gzip compatible.

MSK_COMPRESS_ZSTD

The type of compression used is zstd compatible.

10.4.15 Cone types

MSK_CT_QUAD

The cone is a quadratic cone.

MSK_CT_RQUAD

The cone is a rotated quadratic cone.

MSK_CT_PEXP

A primal exponential cone.

MSK_CT_DEXP

A dual exponential cone.

MSK_CT_PPOW

A primal power cone.

MSK_CT_DPOW

A dual power cone.

MSK_CT_ZERO

The zero cone.

10.4.16 Cone types

MSK_DOMAIN_R

MSK_DOMAIN_RZERO

The zero vector.

MSK_DOMAIN_RPLUS

The positive orthant.

MSK_DOMAIN_RMINUS

The negative orthant.

MSK_DOMAIN_QUADRATIC_CONE

The quadratic cone.

MSK_DOMAIN_RQUADRATIC_CONE

The rotated quadratic cone.

MSK_DOMAIN_PRIMAL_EXP_CONE

The primal exponential cone.

MSK_DOMAIN_DUAL_EXP_CONE

The dual exponential cone.

MSK_DOMAIN_PRIMAL_POWER_CONE

The primal power cone.

MSK_DOMAIN_DUAL_POWER_CONE

The dual power cone.

MSK_DOMAIN_PRIMAL_GEO_MEAN_CONE

The primal geometric mean cone.

MSK_DOMAIN_DUAL_GEO_MEAN_CONE

The dual geometric mean cone.

MSK_DOMAIN_SVEC_PSD_CONE

The vectorized positive semidefinite cone.

10.4.17 Name types

MSK_NAME_TYPE_GEN

General names. However, no duplicate and blank names are allowed.

MSK_NAME_TYPE_MPS

MPS type names.

MSK_NAME_TYPE_LP

LP type names.

10.4.18 Cone types

MSK_SYMMAT_TYPE_SPARSE

Sparse symmetric matrix.

10.4.19 Data format types

MSK_DATA_FORMAT_EXTENSION

The file extension is used to determine the data file format.

MSK_DATA_FORMAT_MPS

The data file is MPS formatted.

MSK_DATA_FORMAT_LP

The data file is LP formatted.

MSK_DATA_FORMAT_OP

The data file is an optimization problem formatted file.

MSK_DATA_FORMAT_FREE_MPS

The data a free MPS formatted file.

MSK_DATA_FORMAT_TASK

Generic task dump file.

MSK_DATA_FORMAT_PTF

(P)retty (T)ext (F)format.

MSK_DATA_FORMAT_CB

Conic benchmark format,

MSK_DATA_FORMAT_JSON_TASK

JSON based task format.

10.4.20 Data format types

MSK_SOL_FORMAT_EXTENSION

The file extension is used to determine the data file format.

MSK_SOL_FORMAT_B

Simple binary format

MSK_SOL_FORMAT_TASK

Tar based format.

MSK_SOL_FORMAT_JSON_TASK

JSON based format.

10.4.21 Double information items

MSK_DINF_ANA_PRO_SCALARIZED_CONSTRAINT_MATRIX_DENSITY

Density percentage of the scalarized constraint matrix.

MSK_DINF_BI_CLEAN_TIME

Time spent within the clean-up phase of the basis identification procedure since its invocation (in seconds).

MSK_DINF_BI_DUAL_TIME

Time spent within the dual phase basis identification procedure since its invocation (in seconds).

MSK_DINF_BI_PRIMAL_TIME

Time spent within the primal phase of the basis identification procedure since its invocation (in seconds).

MSK_DINF_BI_TIME

Time spent within the basis identification procedure since its invocation (in seconds).

MSK_DINF_FOLDING_BI_OPTIMIZE_TIME

TBD

MSK_DINF_FOLDING_BI_UNFOLD_DUAL_TIME

TBD

MSK_DINF_FOLDING_BI_UNFOLD_INITIALIZE_TIME

TBD

MSK_DINF_FOLDING_BI_UNFOLD_PRIMAL_TIME

TBD

MSK_DINF_FOLDING_BI_UNFOLD_TIME

TBD

MSK_DINF_FOLDING_FACTOR

Problem size after folding as a fraction of the original size.

MSK_DINF_FOLDING_TIME

Total time spent in folding for continuous problems (in seconds).

MSK_DINF_INTPNT_DUAL_FEAS

Dual feasibility measure reported by the interior-point optimizer. (For the interior-point optimizer this measure is not directly related to the original problem because a homogeneous model is employed.)

MSK_DINF_INTPNT_DUAL_OBJ

Dual objective value reported by the interior-point optimizer.

MSK_DINF_INTPNT_FACTOR_NUM_FLOPS

An estimate of the number of flops used in the factorization.

MSK_DINF_INTPNT_OPT_STATUS

A measure of optimality of the solution. It should converge to \(+1\) if the problem has a primal-dual optimal solution, and converge to \(-1\) if the problem is (strictly) primal or dual infeasible. If the measure converges to another constant, or fails to settle, the problem is usually ill-posed.

MSK_DINF_INTPNT_ORDER_TIME

Order time (in seconds).

MSK_DINF_INTPNT_PRIMAL_FEAS

Primal feasibility measure reported by the interior-point optimizer. (For the interior-point optimizer this measure is not directly related to the original problem because a homogeneous model is employed).

MSK_DINF_INTPNT_PRIMAL_OBJ

Primal objective value reported by the interior-point optimizer.

MSK_DINF_INTPNT_TIME

Time spent within the interior-point optimizer since its invocation (in seconds).

MSK_DINF_MIO_CLIQUE_SELECTION_TIME

Selection time for clique cuts (in seconds).

MSK_DINF_MIO_CLIQUE_SEPARATION_TIME

Separation time for clique cuts (in seconds).

MSK_DINF_MIO_CMIR_SELECTION_TIME

Selection time for CMIR cuts (in seconds).

MSK_DINF_MIO_CMIR_SEPARATION_TIME

Separation time for CMIR cuts (in seconds).

MSK_DINF_MIO_CONSTRUCT_SOLUTION_OBJ

If MOSEK has successfully constructed an integer feasible solution, then this item contains the optimal objective value corresponding to the feasible solution.

MSK_DINF_MIO_DUAL_BOUND_AFTER_PRESOLVE

Value of the dual bound after presolve but before cut generation.

MSK_DINF_MIO_GMI_SELECTION_TIME

Selection time for GMI cuts (in seconds).

MSK_DINF_MIO_GMI_SEPARATION_TIME

Separation time for GMI cuts (in seconds).

MSK_DINF_MIO_IMPLIED_BOUND_SELECTION_TIME

Selection time for implied bound cuts (in seconds).

MSK_DINF_MIO_IMPLIED_BOUND_SEPARATION_TIME

Separation time for implied bound cuts (in seconds).

MSK_DINF_MIO_INITIAL_FEASIBLE_SOLUTION_OBJ

If the user provided solution was found to be feasible this information item contains it’s objective value.

MSK_DINF_MIO_KNAPSACK_COVER_SELECTION_TIME

Selection time for knapsack cover (in seconds).

MSK_DINF_MIO_KNAPSACK_COVER_SEPARATION_TIME

Separation time for knapsack cover (in seconds).

MSK_DINF_MIO_LIPRO_SELECTION_TIME

Selection time for lift-and-project cuts (in seconds).

MSK_DINF_MIO_LIPRO_SEPARATION_TIME

Separation time for lift-and-project cuts (in seconds).

MSK_DINF_MIO_OBJ_ABS_GAP

Given the mixed-integer optimizer has computed a feasible solution and a bound on the optimal objective value, then this item contains the absolute gap defined by

\[|\mbox{(objective value of feasible solution)}-\mbox{(objective bound)}|.\]

Otherwise it has the value -1.0.

MSK_DINF_MIO_OBJ_BOUND

The best known bound on the objective function. This value is undefined until at least one relaxation has been solved: To see if this is the case check that MSK_IINF_MIO_NUM_RELAX is strictly positive.

MSK_DINF_MIO_OBJ_INT

The primal objective value corresponding to the best integer feasible solution. Please note that at least one integer feasible solution must have been located i.e. check MSK_IINF_MIO_NUM_INT_SOLUTIONS.

MSK_DINF_MIO_OBJ_REL_GAP

Given that the mixed-integer optimizer has computed a feasible solution and a bound on the optimal objective value, then this item contains the relative gap defined by

\[\frac{| \mbox{(objective value of feasible solution)}-\mbox{(objective bound)} | }{\max(\delta,|\mbox{(objective value of feasible solution)}|)}.\]

where \(\delta\) is given by the parameter MSK_DPAR_MIO_REL_GAP_CONST. Otherwise it has the value \(-1.0\).

MSK_DINF_MIO_PROBING_TIME

Total time for probing (in seconds).

MSK_DINF_MIO_ROOT_CUT_SELECTION_TIME

Total time for cut selection (in seconds).

MSK_DINF_MIO_ROOT_CUT_SEPARATION_TIME

Total time for cut separation (in seconds).

MSK_DINF_MIO_ROOT_OPTIMIZER_TIME

Time spent in the contiuous optimizer while processing the root node relaxation (in seconds).

MSK_DINF_MIO_ROOT_PRESOLVE_TIME

Time spent presolving the problem at the root node (in seconds).

MSK_DINF_MIO_ROOT_TIME

Time spent processing the root node (in seconds).

MSK_DINF_MIO_SYMMETRY_DETECTION_TIME

Total time for symmetry detection (in seconds).

MSK_DINF_MIO_SYMMETRY_FACTOR

Degree to which the problem is affected by detected symmetry.

MSK_DINF_MIO_TIME

Time spent in the mixed-integer optimizer (in seconds).

MSK_DINF_MIO_USER_OBJ_CUT

If the objective cut is used, then this information item has the value of the cut.

MSK_DINF_OPTIMIZER_TICKS

Total number of ticks spent in the optimizer since it was invoked. It is strictly negative if it is not available.

MSK_DINF_OPTIMIZER_TIME

Total time spent in the optimizer since it was invoked (in seconds).

MSK_DINF_PRESOLVE_ELI_TIME

Total time spent in the eliminator since the presolve was invoked (in seconds).

MSK_DINF_PRESOLVE_LINDEP_TIME

Total time spent in the linear dependency checker since the presolve was invoked (in seconds).

MSK_DINF_PRESOLVE_TIME

Total time spent in the presolve since it was invoked (in seconds).

MSK_DINF_PRESOLVE_TOTAL_PRIMAL_PERTURBATION

Total perturbation of the bounds of the primal problem.

MSK_DINF_PRIMAL_REPAIR_PENALTY_OBJ

The optimal objective value of the penalty function.

MSK_DINF_QCQO_REFORMULATE_MAX_PERTURBATION

Maximum absolute diagonal perturbation occurring during the QCQO reformulation.

MSK_DINF_QCQO_REFORMULATE_TIME

Time spent with conic quadratic reformulation (in seconds).

MSK_DINF_QCQO_REFORMULATE_WORST_CHOLESKY_COLUMN_SCALING

Worst Cholesky column scaling.

MSK_DINF_QCQO_REFORMULATE_WORST_CHOLESKY_DIAG_SCALING

Worst Cholesky diagonal scaling.

MSK_DINF_READ_DATA_TIME

Time spent reading the data file (in seconds).

MSK_DINF_REMOTE_TIME

The total real time in seconds spent when optimizing on a server by the process performing the optimization on the server (in seconds).

MSK_DINF_SIM_DUAL_TIME

Time spent in the dual simplex optimizer since invoking it (in seconds).

MSK_DINF_SIM_FEAS

Feasibility measure reported by the simplex optimizer.

MSK_DINF_SIM_OBJ

Objective value reported by the simplex optimizer.

MSK_DINF_SIM_PRIMAL_TIME

Time spent in the primal simplex optimizer since invoking it (in seconds).

MSK_DINF_SIM_TIME

Time spent in the simplex optimizer since invoking it (in seconds).

MSK_DINF_SOL_BAS_DUAL_OBJ

Dual objective value of the basic solution. Updated if MSK_IPAR_AUTO_UPDATE_SOL_INFO is set .

MSK_DINF_SOL_BAS_DVIOLCON

Maximal dual bound violation for \(x^c\) in the basic solution. Updated if MSK_IPAR_AUTO_UPDATE_SOL_INFO is set .

MSK_DINF_SOL_BAS_DVIOLVAR

Maximal dual bound violation for \(x^x\) in the basic solution. Updated if MSK_IPAR_AUTO_UPDATE_SOL_INFO is set .

MSK_DINF_SOL_BAS_NRM_BARX

Infinity norm of \(\barX\) in the basic solution.

MSK_DINF_SOL_BAS_NRM_SLC

Infinity norm of \(s_l^c\) in the basic solution.

MSK_DINF_SOL_BAS_NRM_SLX

Infinity norm of \(s_l^x\) in the basic solution.

MSK_DINF_SOL_BAS_NRM_SUC

Infinity norm of \(s_u^c\) in the basic solution.

MSK_DINF_SOL_BAS_NRM_SUX

Infinity norm of \(s_u^X\) in the basic solution.

MSK_DINF_SOL_BAS_NRM_XC

Infinity norm of \(x^c\) in the basic solution.

MSK_DINF_SOL_BAS_NRM_XX

Infinity norm of \(x^x\) in the basic solution.

MSK_DINF_SOL_BAS_NRM_Y

Infinity norm of \(y\) in the basic solution.

MSK_DINF_SOL_BAS_PRIMAL_OBJ

Primal objective value of the basic solution. Updated if MSK_IPAR_AUTO_UPDATE_SOL_INFO is set .

MSK_DINF_SOL_BAS_PVIOLCON

Maximal primal bound violation for \(x^c\) in the basic solution. Updated if MSK_IPAR_AUTO_UPDATE_SOL_INFO is set .

MSK_DINF_SOL_BAS_PVIOLVAR

Maximal primal bound violation for \(x^x\) in the basic solution. Updated if MSK_IPAR_AUTO_UPDATE_SOL_INFO is set .

MSK_DINF_SOL_ITG_NRM_BARX

Infinity norm of \(\barX\) in the integer solution.

MSK_DINF_SOL_ITG_NRM_XC

Infinity norm of \(x^c\) in the integer solution.

MSK_DINF_SOL_ITG_NRM_XX

Infinity norm of \(x^x\) in the integer solution.

MSK_DINF_SOL_ITG_PRIMAL_OBJ

Primal objective value of the integer solution. Updated if MSK_IPAR_AUTO_UPDATE_SOL_INFO is set .

MSK_DINF_SOL_ITG_PVIOLACC

Maximal primal violation for affine conic constraints in the integer solution. Updated if MSK_IPAR_AUTO_UPDATE_SOL_INFO is set .

MSK_DINF_SOL_ITG_PVIOLBARVAR

Maximal primal bound violation for \(\barX\) in the integer solution. Updated if MSK_IPAR_AUTO_UPDATE_SOL_INFO is set .

MSK_DINF_SOL_ITG_PVIOLCON

Maximal primal bound violation for \(x^c\) in the integer solution. Updated if MSK_IPAR_AUTO_UPDATE_SOL_INFO is set .

MSK_DINF_SOL_ITG_PVIOLCONES

Maximal primal violation for primal conic constraints in the integer solution. Updated if MSK_IPAR_AUTO_UPDATE_SOL_INFO is set .

MSK_DINF_SOL_ITG_PVIOLDJC

Maximal primal violation for disjunctive constraints in the integer solution. Updated if MSK_IPAR_AUTO_UPDATE_SOL_INFO is set .

MSK_DINF_SOL_ITG_PVIOLITG

Maximal violation for the integer constraints in the integer solution. Updated if MSK_IPAR_AUTO_UPDATE_SOL_INFO is set .

MSK_DINF_SOL_ITG_PVIOLVAR

Maximal primal bound violation for \(x^x\) in the integer solution. Updated if MSK_IPAR_AUTO_UPDATE_SOL_INFO is set .

MSK_DINF_SOL_ITR_DUAL_OBJ

Dual objective value of the interior-point solution. Updated if MSK_IPAR_AUTO_UPDATE_SOL_INFO is set .

MSK_DINF_SOL_ITR_DVIOLACC

Maximal dual violation for the affine conic constraints in the interior-point solution. Updated if MSK_IPAR_AUTO_UPDATE_SOL_INFO is set .

MSK_DINF_SOL_ITR_DVIOLBARVAR

Maximal dual bound violation for \(\barX\) in the interior-point solution. Updated if MSK_IPAR_AUTO_UPDATE_SOL_INFO is set .

MSK_DINF_SOL_ITR_DVIOLCON

Maximal dual bound violation for \(x^c\) in the interior-point solution. Updated if MSK_IPAR_AUTO_UPDATE_SOL_INFO is set .

MSK_DINF_SOL_ITR_DVIOLCONES

Maximal dual violation for conic constraints in the interior-point solution. Updated if MSK_IPAR_AUTO_UPDATE_SOL_INFO is set .

MSK_DINF_SOL_ITR_DVIOLVAR

Maximal dual bound violation for \(x^x\) in the interior-point solution. Updated if MSK_IPAR_AUTO_UPDATE_SOL_INFO is set .

MSK_DINF_SOL_ITR_NRM_BARS

Infinity norm of \(\barS\) in the interior-point solution.

MSK_DINF_SOL_ITR_NRM_BARX

Infinity norm of \(\barX\) in the interior-point solution.

MSK_DINF_SOL_ITR_NRM_SLC

Infinity norm of \(s_l^c\) in the interior-point solution.

MSK_DINF_SOL_ITR_NRM_SLX

Infinity norm of \(s_l^x\) in the interior-point solution.

MSK_DINF_SOL_ITR_NRM_SNX

Infinity norm of \(s_n^x\) in the interior-point solution.

MSK_DINF_SOL_ITR_NRM_SUC

Infinity norm of \(s_u^c\) in the interior-point solution.

MSK_DINF_SOL_ITR_NRM_SUX

Infinity norm of \(s_u^X\) in the interior-point solution.

MSK_DINF_SOL_ITR_NRM_XC

Infinity norm of \(x^c\) in the interior-point solution.

MSK_DINF_SOL_ITR_NRM_XX

Infinity norm of \(x^x\) in the interior-point solution.

MSK_DINF_SOL_ITR_NRM_Y

Infinity norm of \(y\) in the interior-point solution.

MSK_DINF_SOL_ITR_PRIMAL_OBJ

Primal objective value of the interior-point solution. Updated if MSK_IPAR_AUTO_UPDATE_SOL_INFO is set .

MSK_DINF_SOL_ITR_PVIOLACC

Maximal primal violation for affine conic constraints in the interior-point solution. Updated if MSK_IPAR_AUTO_UPDATE_SOL_INFO is set .

MSK_DINF_SOL_ITR_PVIOLBARVAR

Maximal primal bound violation for \(\barX\) in the interior-point solution. Updated if MSK_IPAR_AUTO_UPDATE_SOL_INFO is set .

MSK_DINF_SOL_ITR_PVIOLCON

Maximal primal bound violation for \(x^c\) in the interior-point solution. Updated if MSK_IPAR_AUTO_UPDATE_SOL_INFO is set .

MSK_DINF_SOL_ITR_PVIOLCONES

Maximal primal violation for conic constraints in the interior-point solution. Updated if MSK_IPAR_AUTO_UPDATE_SOL_INFO is set .

MSK_DINF_SOL_ITR_PVIOLVAR

Maximal primal bound violation for \(x^x\) in the interior-point solution. Updated if MSK_IPAR_AUTO_UPDATE_SOL_INFO is set .

MSK_DINF_TO_CONIC_TIME

Time spent in the last to conic reformulation (in seconds).

MSK_DINF_WRITE_DATA_TIME

Time spent writing the data file (in seconds).

10.4.22 License feature

MSK_FEATURE_PTS

Base system.

MSK_FEATURE_PTON

Conic extension.

10.4.23 Long integer information items.

MSK_LIINF_ANA_PRO_SCALARIZED_CONSTRAINT_MATRIX_NUM_COLUMNS

Number of columns in the scalarized constraint matrix.

MSK_LIINF_ANA_PRO_SCALARIZED_CONSTRAINT_MATRIX_NUM_NZ

Number of non-zero entries in the scalarized constraint matrix.

MSK_LIINF_ANA_PRO_SCALARIZED_CONSTRAINT_MATRIX_NUM_ROWS

Number of rows in the scalarized constraint matrix.

MSK_LIINF_BI_CLEAN_ITER

Number of clean iterations performed in the basis identification.

MSK_LIINF_BI_DUAL_ITER

Number of dual pivots performed in the basis identification.

MSK_LIINF_BI_PRIMAL_ITER

Number of primal pivots performed in the basis identification.

MSK_LIINF_FOLDING_BI_DUAL_ITER

TBD

MSK_LIINF_FOLDING_BI_OPTIMIZER_ITER

TBD

MSK_LIINF_FOLDING_BI_PRIMAL_ITER

TBD

MSK_LIINF_INTPNT_FACTOR_NUM_NZ

Number of non-zeros in factorization.

MSK_LIINF_MIO_ANZ

Number of non-zero entries in the constraint matrix of the problem to be solved by the mixed-integer optimizer.

MSK_LIINF_MIO_FINAL_ANZ

Number of non-zero entries in the constraint matrix of the mixed-integer optimizer’s final problem.

MSK_LIINF_MIO_INTPNT_ITER

Number of interior-point iterations performed by the mixed-integer optimizer.

MSK_LIINF_MIO_NUM_DUAL_ILLPOSED_CER

Number of dual illposed certificates encountered by the mixed-integer optimizer.

MSK_LIINF_MIO_NUM_PRIM_ILLPOSED_CER

Number of primal illposed certificates encountered by the mixed-integer optimizer.

MSK_LIINF_MIO_PRESOLVED_ANZ

Number of non-zero entries in the constraint matrix of the problem after the mixed-integer optimizer’s presolve.

MSK_LIINF_MIO_SIMPLEX_ITER

Number of simplex iterations performed by the mixed-integer optimizer.

MSK_LIINF_RD_NUMACC

Number of affince conic constraints.

MSK_LIINF_RD_NUMANZ

Number of non-zeros in A that is read.

MSK_LIINF_RD_NUMDJC

Number of disjuncive constraints.

MSK_LIINF_RD_NUMQNZ

Number of Q non-zeros.

MSK_LIINF_SIMPLEX_ITER

Number of iterations performed by the simplex optimizer.

10.4.24 Integer information items.

MSK_IINF_ANA_PRO_NUM_CON

Number of constraints in the problem.

MSK_IINF_ANA_PRO_NUM_CON_EQ

Number of equality constraints.

MSK_IINF_ANA_PRO_NUM_CON_FR

Number of unbounded constraints.

MSK_IINF_ANA_PRO_NUM_CON_LO

Number of constraints with a lower bound and an infinite upper bound.

MSK_IINF_ANA_PRO_NUM_CON_RA

Number of constraints with finite lower and upper bounds.

MSK_IINF_ANA_PRO_NUM_CON_UP

Number of constraints with an upper bound and an infinite lower bound.

MSK_IINF_ANA_PRO_NUM_VAR

Number of variables in the problem.

MSK_IINF_ANA_PRO_NUM_VAR_BIN

Number of binary (0-1) variables.

MSK_IINF_ANA_PRO_NUM_VAR_CONT

Number of continuous variables.

MSK_IINF_ANA_PRO_NUM_VAR_EQ

Number of fixed variables.

MSK_IINF_ANA_PRO_NUM_VAR_FR

Number of free variables.

MSK_IINF_ANA_PRO_NUM_VAR_INT

Number of general integer variables.

MSK_IINF_ANA_PRO_NUM_VAR_LO

Number of variables with a lower bound and an infinite upper bound.

MSK_IINF_ANA_PRO_NUM_VAR_RA

Number of variables with finite lower and upper bounds.

MSK_IINF_ANA_PRO_NUM_VAR_UP

Number of variables with an upper bound and an infinite lower bound.

MSK_IINF_FOLDING_APPLIED

Non-zero if folding was exploited.

MSK_IINF_INTPNT_FACTOR_DIM_DENSE

Dimension of the dense sub system in factorization.

MSK_IINF_INTPNT_ITER

Number of interior-point iterations since invoking the interior-point optimizer.

MSK_IINF_INTPNT_NUM_THREADS

Number of threads that the interior-point optimizer is using.

MSK_IINF_INTPNT_SOLVE_DUAL

Non-zero if the interior-point optimizer is solving the dual problem.

MSK_IINF_MIO_ABSGAP_SATISFIED

Non-zero if absolute gap is within tolerances.

MSK_IINF_MIO_CLIQUE_TABLE_SIZE

Size of the clique table.

MSK_IINF_MIO_CONSTRUCT_SOLUTION

This item informs if MOSEK constructed an initial integer feasible solution.

• -1: tried, but failed,

• 0: no partial solution supplied by the user,

• 1: constructed feasible solution.

MSK_IINF_MIO_FINAL_NUMBIN

Number of binary variables in the mixed-integer optimizer’s final problem.

MSK_IINF_MIO_FINAL_NUMBINCONEVAR

Number of binary cone variables in the mixed-integer optimizer’s final problem.

MSK_IINF_MIO_FINAL_NUMCON

Number of constraints in the mixed-integer optimizer’s final problem.

MSK_IINF_MIO_FINAL_NUMCONE

Number of cones in the mixed-integer optimizer’s final problem.

MSK_IINF_MIO_FINAL_NUMCONEVAR

Number of cone variables in the mixed-integer optimizer’s final problem.

MSK_IINF_MIO_FINAL_NUMCONT

Number of continuous variables in the mixed-integer optimizer’s final problem.

MSK_IINF_MIO_FINAL_NUMCONTCONEVAR

Number of continuous cone variables in the mixed-integer optimizer’s final problem.

MSK_IINF_MIO_FINAL_NUMDEXPCONES

Number of dual exponential cones in the mixed-integer optimizer’s final problem.

MSK_IINF_MIO_FINAL_NUMDJC

Number of disjunctive constraints in the mixed-integer optimizer’s final problem.

MSK_IINF_MIO_FINAL_NUMDPOWCONES

Number of dual power cones in the mixed-integer optimizer’s final problem.

MSK_IINF_MIO_FINAL_NUMINT

Number of integer variables in the mixed-integer optimizer’s final problem.

MSK_IINF_MIO_FINAL_NUMINTCONEVAR

Number of integer cone variables in the mixed-integer optimizer’s final problem.

MSK_IINF_MIO_FINAL_NUMPEXPCONES

Number of primal exponential cones in the mixed-integer optimizer’s final problem.

MSK_IINF_MIO_FINAL_NUMPPOWCONES

Number of primal power cones in the mixed-integer optimizer’s final problem.

MSK_IINF_MIO_FINAL_NUMQCONES

Number of quadratic cones in the mixed-integer optimizer’s final problem.

MSK_IINF_MIO_FINAL_NUMRQCONES

Number of rotated quadratic cones in the mixed-integer optimizer’s final problem.

MSK_IINF_MIO_FINAL_NUMVAR

Number of variables in the mixed-integer optimizer’s final problem.

MSK_IINF_MIO_INITIAL_FEASIBLE_SOLUTION

This item informs if MOSEK found the solution provided by the user to be feasible

• 0: solution provided by the user was not found to be feasible for the current problem,

• 1: user provided solution was found to be feasible.

MSK_IINF_MIO_NODE_DEPTH

Depth of the last node solved.

MSK_IINF_MIO_NUM_ACTIVE_NODES

Number of active branch and bound nodes.

MSK_IINF_MIO_NUM_ACTIVE_ROOT_CUTS

Number of active cuts in the final relaxation after the mixed-integer optimizer’s root cut generation.

MSK_IINF_MIO_NUM_BLOCKS_SOLVED_IN_BB

Number of independent decomposition blocks solved though a dedicated algorithm.

MSK_IINF_MIO_NUM_BLOCKS_SOLVED_IN_PRESOLVE

Number of independent decomposition blocks solved during presolve.

MSK_IINF_MIO_NUM_BRANCH

Number of branches performed during the optimization.

MSK_IINF_MIO_NUM_INT_SOLUTIONS

Number of integer feasible solutions that have been found.

MSK_IINF_MIO_NUM_RELAX

Number of relaxations solved during the optimization.

MSK_IINF_MIO_NUM_REPEATED_PRESOLVE

Number of times presolve was repeated at root.

MSK_IINF_MIO_NUM_RESTARTS

Number of restarts performed during the optimization.

MSK_IINF_MIO_NUM_ROOT_CUT_ROUNDS

Number of cut separation rounds at the root node of the mixed-integer optimizer.

MSK_IINF_MIO_NUM_SELECTED_CLIQUE_CUTS

Number of clique cuts selected to be included in the relaxation.

MSK_IINF_MIO_NUM_SELECTED_CMIR_CUTS

Number of Complemented Mixed Integer Rounding (CMIR) cuts selected to be included in the relaxation.

MSK_IINF_MIO_NUM_SELECTED_GOMORY_CUTS

Number of Gomory cuts selected to be included in the relaxation.

MSK_IINF_MIO_NUM_SELECTED_IMPLIED_BOUND_CUTS

Number of implied bound cuts selected to be included in the relaxation.

MSK_IINF_MIO_NUM_SELECTED_KNAPSACK_COVER_CUTS

Number of clique cuts selected to be included in the relaxation.

MSK_IINF_MIO_NUM_SELECTED_LIPRO_CUTS

Number of lift-and-project cuts selected to be included in the relaxation.

MSK_IINF_MIO_NUM_SEPARATED_CLIQUE_CUTS

Number of separated clique cuts.

MSK_IINF_MIO_NUM_SEPARATED_CMIR_CUTS

Number of separated Complemented Mixed Integer Rounding (CMIR) cuts.

MSK_IINF_MIO_NUM_SEPARATED_GOMORY_CUTS

Number of separated Gomory cuts.

MSK_IINF_MIO_NUM_SEPARATED_IMPLIED_BOUND_CUTS

Number of separated implied bound cuts.

MSK_IINF_MIO_NUM_SEPARATED_KNAPSACK_COVER_CUTS

Number of separated clique cuts.

MSK_IINF_MIO_NUM_SEPARATED_LIPRO_CUTS

Number of separated lift-and-project cuts.

MSK_IINF_MIO_NUM_SOLVED_NODES

Number of branch and bounds nodes solved in the main branch and bound tree.

MSK_IINF_MIO_NUMBIN

Number of binary variables in the problem to be solved by the mixed-integer optimizer.

MSK_IINF_MIO_NUMBINCONEVAR

Number of binary cone variables in the problem to be solved by the mixed-integer optimizer.

MSK_IINF_MIO_NUMCON

Number of constraints in the problem to be solved by the mixed-integer optimizer.

MSK_IINF_MIO_NUMCONE

Number of cones in the problem to be solved by the mixed-integer optimizer.

MSK_IINF_MIO_NUMCONEVAR

Number of cone variables in the problem to be solved by the mixed-integer optimizer.

MSK_IINF_MIO_NUMCONT

Number of continuous variables in the problem to be solved by the mixed-integer optimizer.

MSK_IINF_MIO_NUMCONTCONEVAR

Number of continuous cone variables in the problem to be solved by the mixed-integer optimizer.

MSK_IINF_MIO_NUMDEXPCONES

Number of dual exponential cones in the problem to be solved by the mixed-integer optimizer.

MSK_IINF_MIO_NUMDJC

Number of disjunctive constraints in the problem to be solved by the mixed-integer optimizer.

MSK_IINF_MIO_NUMDPOWCONES

Number of dual power cones in the problem to be solved by the mixed-integer optimizer.

MSK_IINF_MIO_NUMINT

Number of integer variables in the problem to be solved by the mixed-integer optimizer.

MSK_IINF_MIO_NUMINTCONEVAR

Number of integer cone variables in the problem to be solved by the mixed-integer optimizer.

MSK_IINF_MIO_NUMPEXPCONES

Number of primal exponential cones in the problem to be solved by the mixed-integer optimizer.

MSK_IINF_MIO_NUMPPOWCONES

Number of primal power cones in the problem to be solved by the mixed-integer optimizer.

MSK_IINF_MIO_NUMQCONES

Number of quadratic cones in the problem to be solved by the mixed-integer optimizer.

MSK_IINF_MIO_NUMRQCONES

Number of rotated quadratic cones in the problem to be solved by the mixed-integer optimizer.

MSK_IINF_MIO_NUMVAR

Number of variables in the problem to be solved by the mixed-integer optimizer.

MSK_IINF_MIO_OBJ_BOUND_DEFINED

Non-zero if a valid objective bound has been found, otherwise zero.

MSK_IINF_MIO_PRESOLVED_NUMBIN

Number of binary variables in the problem after the mixed-integer optimizer’s presolve.

MSK_IINF_MIO_PRESOLVED_NUMBINCONEVAR

Number of binary cone variables in the problem after the mixed-integer optimizer’s presolve.

MSK_IINF_MIO_PRESOLVED_NUMCON

Number of constraints in the problem after the mixed-integer optimizer’s presolve.

MSK_IINF_MIO_PRESOLVED_NUMCONE

Number of cones in the problem after the mixed-integer optimizer’s presolve.

MSK_IINF_MIO_PRESOLVED_NUMCONEVAR

Number of cone variables in the problem after the mixed-integer optimizer’s presolve.

MSK_IINF_MIO_PRESOLVED_NUMCONT

Number of continuous variables in the problem after the mixed-integer optimizer’s presolve.

MSK_IINF_MIO_PRESOLVED_NUMCONTCONEVAR

Number of continuous cone variables in the problem after the mixed-integer optimizer’s presolve.

MSK_IINF_MIO_PRESOLVED_NUMDEXPCONES

Number of dual exponential cones in the problem after the mixed-integer optimizer’s presolve.

MSK_IINF_MIO_PRESOLVED_NUMDJC

Number of disjunctive constraints in the problem after the mixed-integer optimizer’s presolve.

MSK_IINF_MIO_PRESOLVED_NUMDPOWCONES

Number of dual power cones in the problem after the mixed-integer optimizer’s presolve.

MSK_IINF_MIO_PRESOLVED_NUMINT

Number of integer variables in the problem after the mixed-integer optimizer’s presolve.

MSK_IINF_MIO_PRESOLVED_NUMINTCONEVAR

Number of integer cone variables in the problem after the mixed-integer optimizer’s presolve.

MSK_IINF_MIO_PRESOLVED_NUMPEXPCONES

Number of primal exponential cones in the problem after the mixed-integer optimizer’s presolve.

MSK_IINF_MIO_PRESOLVED_NUMPPOWCONES

Number of primal power cones in the problem after the mixed-integer optimizer’s presolve.

MSK_IINF_MIO_PRESOLVED_NUMQCONES

Number of quadratic cones in the problem after the mixed-integer optimizer’s presolve.

MSK_IINF_MIO_PRESOLVED_NUMRQCONES

Number of rotated quadratic cones in the problem after the mixed-integer optimizer’s presolve.

MSK_IINF_MIO_PRESOLVED_NUMVAR

Number of variables in the problem after the mixed-integer optimizer’s presolve.

MSK_IINF_MIO_RELGAP_SATISFIED

Non-zero if relative gap is within tolerances.

MSK_IINF_MIO_TOTAL_NUM_SELECTED_CUTS

Total number of cuts selected to be included in the relaxation by the mixed-integer optimizer.

MSK_IINF_MIO_TOTAL_NUM_SEPARATED_CUTS

Total number of cuts separated by the mixed-integer optimizer.

MSK_IINF_MIO_USER_OBJ_CUT

If it is non-zero, then the objective cut is used.

MSK_IINF_OPT_NUMCON

Number of constraints in the problem solved when the optimizer is called.

MSK_IINF_OPT_NUMVAR

Number of variables in the problem solved when the optimizer is called

MSK_IINF_OPTIMIZE_RESPONSE

The response code returned by optimize.

MSK_IINF_PRESOLVE_NUM_PRIMAL_PERTURBATIONS

Number perturbations to thhe bounds of the primal problem.

MSK_IINF_PURIFY_DUAL_SUCCESS

Is nonzero if the dual solution is purified.

MSK_IINF_PURIFY_PRIMAL_SUCCESS

Is nonzero if the primal solution is purified.

MSK_IINF_RD_NUMBARVAR

Number of symmetric variables read.

MSK_IINF_RD_NUMCON

Number of constraints read.

MSK_IINF_RD_NUMCONE

Number of conic constraints read.

MSK_IINF_RD_NUMINTVAR

Number of integer-constrained variables read.

MSK_IINF_RD_NUMQ

Number of nonempty Q matrices read.

MSK_IINF_RD_NUMVAR

Number of variables read.

MSK_IINF_RD_PROTYPE

Problem type.

MSK_IINF_SIM_DUAL_DEG_ITER

The number of dual degenerate iterations.

MSK_IINF_SIM_DUAL_HOTSTART

If 1 then the dual simplex algorithm is solving from an advanced basis.

MSK_IINF_SIM_DUAL_HOTSTART_LU

If 1 then a valid basis factorization of full rank was located and used by the dual simplex algorithm.

MSK_IINF_SIM_DUAL_INF_ITER

The number of iterations taken with dual infeasibility.

MSK_IINF_SIM_DUAL_ITER

Number of dual simplex iterations during the last optimization.

MSK_IINF_SIM_NUMCON

Number of constraints in the problem solved by the simplex optimizer.

MSK_IINF_SIM_NUMVAR

Number of variables in the problem solved by the simplex optimizer.

MSK_IINF_SIM_PRIMAL_DEG_ITER

The number of primal degenerate iterations.

MSK_IINF_SIM_PRIMAL_HOTSTART

If 1 then the primal simplex algorithm is solving from an advanced basis.

MSK_IINF_SIM_PRIMAL_HOTSTART_LU

If 1 then a valid basis factorization of full rank was located and used by the primal simplex algorithm.

MSK_IINF_SIM_PRIMAL_INF_ITER

The number of iterations taken with primal infeasibility.

MSK_IINF_SIM_PRIMAL_ITER

Number of primal simplex iterations during the last optimization.

MSK_IINF_SIM_SOLVE_DUAL

Is non-zero if dual problem is solved.

MSK_IINF_SOL_BAS_PROSTA

Problem status of the basic solution. Updated after each optimization.

MSK_IINF_SOL_BAS_SOLSTA

Solution status of the basic solution. Updated after each optimization.

MSK_IINF_SOL_ITG_PROSTA

Problem status of the integer solution. Updated after each optimization.

MSK_IINF_SOL_ITG_SOLSTA

Solution status of the integer solution. Updated after each optimization.

MSK_IINF_SOL_ITR_PROSTA

Problem status of the interior-point solution. Updated after each optimization.

MSK_IINF_SOL_ITR_SOLSTA

Solution status of the interior-point solution. Updated after each optimization.

MSK_IINF_STO_NUM_A_REALLOC

Number of times the storage for storing \(A\) has been changed. A large value may indicates that memory fragmentation may occur.

10.4.25 Information item types

MSK_INF_DOU_TYPE

Is a double information type.

MSK_INF_INT_TYPE

Is an integer.

MSK_INF_LINT_TYPE

Is a long integer.

10.4.26 Input/output modes

MSK_IOMODE_READ

The file is read-only.

MSK_IOMODE_WRITE

The file is write-only. If the file exists then it is truncated when it is opened. Otherwise it is created when it is opened.

MSK_IOMODE_READWRITE

The file is to read and write.

10.4.27 Specifies the branching direction.

MSK_BRANCH_DIR_FREE

The mixed-integer optimizer decides which branch to choose.

MSK_BRANCH_DIR_UP

The mixed-integer optimizer always chooses the up branch first.

MSK_BRANCH_DIR_DOWN

The mixed-integer optimizer always chooses the down branch first.

MSK_BRANCH_DIR_NEAR

Branch in direction nearest to selected fractional variable.

MSK_BRANCH_DIR_FAR

Branch in direction farthest from selected fractional variable.

MSK_BRANCH_DIR_ROOT_LP

Chose direction based on root lp value of selected variable.

MSK_BRANCH_DIR_GUIDED

Branch in direction of current incumbent.

MSK_BRANCH_DIR_PSEUDOCOST

Branch based on the pseudocost of the variable.

10.4.28 Specifies the reformulation method for mixed-integer quadratic problems.

MSK_MIO_QCQO_REFORMULATION_METHOD_FREE

The mixed-integer optimizer decides which reformulation method to apply.

MSK_MIO_QCQO_REFORMULATION_METHOD_NONE

No reformulation method is applied.

MSK_MIO_QCQO_REFORMULATION_METHOD_LINEARIZATION

A reformulation via linearization is applied.

MSK_MIO_QCQO_REFORMULATION_METHOD_EIGEN_VAL_METHOD

The eigenvalue method is applied.

MSK_MIO_QCQO_REFORMULATION_METHOD_DIAG_SDP

A perturbation of matrix diagonals via the solution of SDPs is applied.

MSK_MIO_QCQO_REFORMULATION_METHOD_RELAX_SDP

A Reformulation based on the solution of an SDP-relaxation of the problem is applied.

10.4.29 Specifies the problem data permutation method for mixed-integer problems.

MSK_MIO_DATA_PERMUTATION_METHOD_NONE

No problem data permutation is applied.

MSK_MIO_DATA_PERMUTATION_METHOD_CYCLIC_SHIFT

A random cyclic shift is applied to permute the problem data.

MSK_MIO_DATA_PERMUTATION_METHOD_RANDOM

A random permutation is applied to the problem data.

10.4.30 Continuous mixed-integer solution type

MSK_MIO_CONT_SOL_NONE

No interior-point or basic solution are reported when the mixed-integer optimizer is used.

MSK_MIO_CONT_SOL_ROOT

The reported interior-point and basic solutions are a solution to the root node problem when mixed-integer optimizer is used.

MSK_MIO_CONT_SOL_ITG

The reported interior-point and basic solutions are a solution to the problem with all integer variables fixed at the value they have in the integer solution. A solution is only reported in case the problem has a primal feasible solution.

MSK_MIO_CONT_SOL_ITG_REL

In case the problem is primal feasible then the reported interior-point and basic solutions are a solution to the problem with all integer variables fixed at the value they have in the integer solution. If the problem is primal infeasible, then the solution to the root node problem is reported.

10.4.31 Integer restrictions

MSK_MIO_MODE_IGNORED

The integer constraints are ignored and the problem is solved as a continuous problem.

MSK_MIO_MODE_SATISFIED

Integer restrictions should be satisfied.

10.4.32 Mixed-integer node selection types

MSK_MIO_NODE_SELECTION_FREE

The optimizer decides the node selection strategy.

MSK_MIO_NODE_SELECTION_FIRST

The optimizer employs a depth first node selection strategy.

MSK_MIO_NODE_SELECTION_BEST

The optimizer employs a best bound node selection strategy.

MSK_MIO_NODE_SELECTION_PSEUDO

The optimizer employs selects the node based on a pseudo cost estimate.

10.4.33 Mixed-integer variable selection types

MSK_MIO_VAR_SELECTION_FREE

The optimizer decides the variable selection strategy.

MSK_MIO_VAR_SELECTION_PSEUDOCOST

The optimizer employs pseudocost variable selection.

MSK_MIO_VAR_SELECTION_STRONG

The optimizer employs strong branching varfiable selection

10.4.34 MPS file format type

MSK_MPS_FORMAT_STRICT

It is assumed that the input file satisfies the MPS format strictly.

MSK_MPS_FORMAT_RELAXED

It is assumed that the input file satisfies a slightly relaxed version of the MPS format.

MSK_MPS_FORMAT_FREE

It is assumed that the input file satisfies the free MPS format. This implies that spaces are not allowed in names. Otherwise the format is free.

MSK_MPS_FORMAT_CPLEX

The CPLEX compatible version of the MPS format is employed.

10.4.35 Objective sense types

MSK_OBJECTIVE_SENSE_MINIMIZE

The problem should be minimized.

MSK_OBJECTIVE_SENSE_MAXIMIZE

The problem should be maximized.

10.4.36 On/off

MSK_ON

Switch the option on.

MSK_OFF

Switch the option off.

10.4.37 Optimizer types

MSK_OPTIMIZER_CONIC

The optimizer for problems having conic constraints.

MSK_OPTIMIZER_DUAL_SIMPLEX

The dual simplex optimizer is used.

MSK_OPTIMIZER_FREE

The optimizer is chosen automatically.

MSK_OPTIMIZER_FREE_SIMPLEX

One of the simplex optimizers is used.

MSK_OPTIMIZER_INTPNT

The interior-point optimizer is used.

MSK_OPTIMIZER_MIXED_INT

The mixed-integer optimizer.

MSK_OPTIMIZER_NEW_DUAL_SIMPLEX

The new dual simplex optimizer is used.

MSK_OPTIMIZER_NEW_PRIMAL_SIMPLEX

The new primal simplex optimizer is used. It is not recommended to use this option.

MSK_OPTIMIZER_PRIMAL_SIMPLEX

The primal simplex optimizer is used.

10.4.38 Ordering strategies

MSK_ORDER_METHOD_FREE

The ordering method is chosen automatically.

MSK_ORDER_METHOD_APPMINLOC

Approximate minimum local fill-in ordering is employed.

MSK_ORDER_METHOD_EXPERIMENTAL

This option should not be used.

MSK_ORDER_METHOD_TRY_GRAPHPAR

Always try the graph partitioning based ordering.

MSK_ORDER_METHOD_FORCE_GRAPHPAR

Always use the graph partitioning based ordering even if it is worse than the approximate minimum local fill ordering.

MSK_ORDER_METHOD_NONE

No ordering is used. Note using this value almost always leads to a significantly slow down.

10.4.39 Presolve method.

MSK_PRESOLVE_MODE_OFF

The problem is not presolved before it is optimized.

MSK_PRESOLVE_MODE_ON

The problem is presolved before it is optimized.

MSK_PRESOLVE_MODE_FREE

It is decided automatically whether to presolve before the problem is optimized.

10.4.40 Method of folding (symmetry detection for continuous problems).

MSK_FOLDING_MODE_OFF

Disabled.

MSK_FOLDING_MODE_FREE

The solver decides on the usage and amount of folding.

MSK_FOLDING_MODE_FREE_UNLESS_BASIC

If only the interior-point solution is requested then the solver decides; if the basic solution is requested then folding is disabled.

MSK_FOLDING_MODE_FORCE

Full folding is always performed regardless of workload.

10.4.41 Parameter type

MSK_PAR_INVALID_TYPE

Not a valid parameter.

MSK_PAR_DOU_TYPE

Is a double parameter.

MSK_PAR_INT_TYPE

Is an integer parameter.

MSK_PAR_STR_TYPE

Is a string parameter.

10.4.42 Problem data items

MSK_PI_VAR

Item is a variable.

MSK_PI_CON

Item is a constraint.

MSK_PI_CONE

Item is a cone.

10.4.43 Problem types

MSK_PROBTYPE_LO

The problem is a linear optimization problem.

MSK_PROBTYPE_QO

The problem is a quadratic optimization problem.

MSK_PROBTYPE_QCQO

The problem is a quadratically constrained optimization problem.

MSK_PROBTYPE_CONIC

A conic optimization.

MSK_PROBTYPE_MIXED

General nonlinear constraints and conic constraints. This combination can not be solved by MOSEK.

10.4.44 Problem status keys

MSK_PRO_STA_UNKNOWN

Unknown problem status.

MSK_PRO_STA_PRIM_AND_DUAL_FEAS

The problem is primal and dual feasible.

MSK_PRO_STA_PRIM_FEAS

The problem is primal feasible.

MSK_PRO_STA_DUAL_FEAS

The problem is dual feasible.

MSK_PRO_STA_PRIM_INFEAS

The problem is primal infeasible.

MSK_PRO_STA_DUAL_INFEAS

The problem is dual infeasible.

MSK_PRO_STA_PRIM_AND_DUAL_INFEAS

The problem is primal and dual infeasible.

MSK_PRO_STA_ILL_POSED

The problem is ill-posed. For example, it may be primal and dual feasible but have a positive duality gap.

MSK_PRO_STA_PRIM_INFEAS_OR_UNBOUNDED

The problem is either primal infeasible or unbounded. This may occur for mixed-integer problems.

10.4.45 Response code type

MSK_RESPONSE_OK

The response code is OK.

MSK_RESPONSE_WRN

The response code is a warning.

MSK_RESPONSE_TRM

The response code is an optimizer termination status.

MSK_RESPONSE_ERR

The response code is an error.

MSK_RESPONSE_UNK

The response code does not belong to any class.

10.4.46 Scaling type

MSK_SCALING_FREE

The optimizer chooses the scaling heuristic.

MSK_SCALING_NONE

No scaling is performed.

10.4.47 Scaling method

MSK_SCALING_METHOD_POW2

Scales only with power of 2 leaving the mantissa untouched.

MSK_SCALING_METHOD_FREE

The optimizer chooses the scaling heuristic.

10.4.48 Sensitivity types

MSK_SENSITIVITY_TYPE_BASIS

Basis sensitivity analysis is performed.

10.4.49 Simplex selection strategy

MSK_SIM_SELECTION_FREE

The optimizer chooses the pricing strategy.

MSK_SIM_SELECTION_FULL

The optimizer uses full pricing.

MSK_SIM_SELECTION_ASE

The optimizer uses approximate steepest-edge pricing.

MSK_SIM_SELECTION_DEVEX

The optimizer uses devex steepest-edge pricing (or if it is not available an approximate steep-edge selection).

MSK_SIM_SELECTION_SE

The optimizer uses steepest-edge selection (or if it is not available an approximate steep-edge selection).

MSK_SIM_SELECTION_PARTIAL

The optimizer uses a partial selection approach. The approach is usually beneficial if the number of variables is much larger than the number of constraints.

10.4.50 Solution items

MSK_SOL_ITEM_XC

Solution for the constraints.

MSK_SOL_ITEM_XX

Variable solution.

MSK_SOL_ITEM_Y

Lagrange multipliers for equations.

MSK_SOL_ITEM_SLC

Lagrange multipliers for lower bounds on the constraints.

MSK_SOL_ITEM_SUC

Lagrange multipliers for upper bounds on the constraints.

MSK_SOL_ITEM_SLX

Lagrange multipliers for lower bounds on the variables.

MSK_SOL_ITEM_SUX

Lagrange multipliers for upper bounds on the variables.

MSK_SOL_ITEM_SNX

Lagrange multipliers corresponding to the conic constraints on the variables.

10.4.51 Solution status keys

MSK_SOL_STA_UNKNOWN

Status of the solution is unknown.

MSK_SOL_STA_OPTIMAL

The solution is optimal.

MSK_SOL_STA_PRIM_FEAS

The solution is primal feasible.

MSK_SOL_STA_DUAL_FEAS

The solution is dual feasible.

MSK_SOL_STA_PRIM_AND_DUAL_FEAS

The solution is both primal and dual feasible.

MSK_SOL_STA_PRIM_INFEAS_CER

The solution is a certificate of primal infeasibility.

MSK_SOL_STA_DUAL_INFEAS_CER

The solution is a certificate of dual infeasibility.

MSK_SOL_STA_PRIM_ILLPOSED_CER

The solution is a certificate that the primal problem is illposed.

MSK_SOL_STA_DUAL_ILLPOSED_CER

The solution is a certificate that the dual problem is illposed.

MSK_SOL_STA_INTEGER_OPTIMAL

The primal solution is integer optimal.

10.4.52 Solution types

MSK_SOL_BAS

The basic solution.

MSK_SOL_ITR

The interior solution.

MSK_SOL_ITG

The integer solution.

10.4.53 Solve primal or dual form

MSK_SOLVE_FREE

The optimizer is free to solve either the primal or the dual problem.

MSK_SOLVE_PRIMAL

The optimizer should solve the primal problem.

MSK_SOLVE_DUAL

The optimizer should solve the dual problem.

10.4.54 Status keys

MSK_SK_UNK

The status for the constraint or variable is unknown.

MSK_SK_BAS

The constraint or variable is in the basis.

MSK_SK_SUPBAS

The constraint or variable is super basic.

MSK_SK_LOW

The constraint or variable is at its lower bound.

MSK_SK_UPR

The constraint or variable is at its upper bound.

MSK_SK_FIX

The constraint or variable is fixed.

MSK_SK_INF

The constraint or variable is infeasible in the bounds.

10.4.55 Starting point types

MSK_STARTING_POINT_FREE

The starting point is chosen automatically.

MSK_STARTING_POINT_GUESS

The optimizer guesses a starting point.

MSK_STARTING_POINT_CONSTANT

The optimizer constructs a starting point by assigning a constant value to all primal and dual variables. This starting point is normally robust.

10.4.56 Stream types

MSK_STREAM_LOG

Log stream. Contains the aggregated contents of all other streams. This means that a message written to any other stream will also be written to this stream.

MSK_STREAM_MSG

Message stream. Log information relating to performance and progress of the optimization is written to this stream.

MSK_STREAM_ERR

Error stream. Error messages are written to this stream.

MSK_STREAM_WRN

Warning stream. Warning messages are written to this stream.

10.4.57 Integer values

MSK_MAX_STR_LEN

Maximum string length allowed in MOSEK.

MSK_LICENSE_BUFFER_LENGTH

The length of a license key buffer.

10.4.58 Variable types

MSK_VAR_TYPE_CONT

Is a continuous variable.

MSK_VAR_TYPE_INT

Is an integer variable.