I solved my semidefinite programming by mosek and use lots of constraints. They are about n / 2 semidefinite constraints with n around 30 and thousands of linear constraints.
After solving that, the solver told me the STATUS is solved and provided a nice answer. But now, I am wondering the correctness of the answer and try to check it by figuring out all primal and dual constraints to ensure the answer is optimal.
How could I do for this?
Here is one of my result.
Calling Mosek 9.1.9: 27336 variables, 1442 equality constraints
For improved efficiency, Mosek is solving the dual problem.
MOSEK Version 9.1.9 (Build date: 2019-11-21 11:34:40)
Copyright © MOSEK ApS, Denmark. WWW: mosek.com
Platform: Windows/64-X86
MOSEK warning 52: A numerically large lower bound value -1.3e+08 is specified for constraint ‘’ (0).
MOSEK warning 53: A numerically large upper bound value -1.3e+08 is specified for constraint ‘’ (0).
Problem
Name :
Objective sense : min
Type : CONIC (conic optimization problem)
Constraints : 1442
Cones : 0
Scalar variables : 6689
Matrix variables : 14
Integer variables : 0
Optimizer started.
Presolve started.
Linear dependency checker started.
Linear dependency checker terminated.
Eliminator started.
Freed constraints in eliminator : 0
Eliminator terminated.
Eliminator started.
Freed constraints in eliminator : 284
Eliminator terminated.
Eliminator - tries : 2 time : 0.00
Lin. dep. - tries : 1 time : 0.02
Lin. dep. - number : 0
Presolve terminated. Time: 0.08
Problem
Name :
Objective sense : min
Type : CONIC (conic optimization problem)
Constraints : 1442
Cones : 0
Scalar variables : 6689
Matrix variables : 14
Integer variables : 0
Optimizer - threads : 2
Optimizer - solved problem : the primal
Optimizer - Constraints : 409
Optimizer - Cones : 1
Optimizer - Scalar variables : 1292 conic : 371
Optimizer - Semi-definite variables: 14 scalarized : 20647
Factor - setup time : 0.01 dense det. time : 0.00
Factor - ML order time : 0.00 GP order time : 0.00
Factor - nonzeros before factor : 4.55e+04 after factor : 6.03e+04
Factor - dense dim. : 2 flops : 2.17e+07
ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME
0 1.9e+00 1.0e+00 2.0e+00 0.00e+00 1.000000000e+00 0.000000000e+00 1.0e+00 0.13
1 1.6e+00 8.2e-01 1.8e+00 -2.66e-01 1.175428946e+00 3.378814873e-01 8.2e-01 0.33
2 9.6e-01 5.0e-01 1.4e+00 -4.30e-01 1.884709630e+00 1.664163271e+00 5.0e-01 0.34
3 2.2e-01 1.1e-01 7.6e-01 -7.67e-01 1.107722909e+01 1.925567650e+01 1.1e-01 0.38
4 3.5e-02 1.8e-02 4.1e-01 -1.26e+00 1.252747523e+02 2.461352726e+02 1.8e-02 0.39
5 5.2e-03 2.7e-03 1.6e-01 -1.23e+00 9.351506857e+02 1.863989678e+03 2.7e-03 0.41
6 9.6e-04 5.0e-04 6.8e-02 -1.15e+00 5.213633755e+03 9.856640440e+03 5.0e-04 0.42
7 4.8e-04 2.5e-04 6.5e-03 4.01e-01 6.950408531e+03 7.117574678e+03 2.5e-04 0.45
8 1.6e-04 8.1e-05 1.5e-03 1.08e+00 5.557091035e+03 5.644764620e+03 8.1e-05 0.47
9 9.4e-05 4.9e-05 8.0e-04 1.71e+00 4.273216562e+03 4.340881298e+03 4.9e-05 0.48
10 3.0e-05 1.5e-05 1.6e-04 1.77e+00 3.625480516e+03 3.652738907e+03 1.5e-05 0.52
11 1.6e-05 8.4e-06 6.1e-05 1.37e+00 3.432214778e+03 3.445428180e+03 8.4e-06 0.53
12 6.7e-06 3.5e-06 1.3e-05 1.66e+00 3.281632721e+03 3.285215331e+03 3.5e-06 0.55
13 5.1e-06 2.7e-06 8.3e-06 1.58e+00 3.235757321e+03 3.238144462e+03 2.7e-06 0.58
14 1.3e-06 6.8e-07 8.4e-07 1.50e+00 3.185035440e+03 3.185415300e+03 6.8e-07 0.59
15 5.3e-07 2.7e-07 1.9e-07 1.41e+00 3.175260609e+03 3.175374120e+03 2.7e-07 0.61
16 1.4e-07 7.3e-08 1.7e-08 1.44e+00 3.171203561e+03 3.171217118e+03 7.3e-08 0.63
17 7.2e-08 3.7e-08 5.5e-09 1.52e+00 3.170505129e+03 3.170510531e+03 3.7e-08 0.66
18 1.8e-08 9.0e-09 5.6e-10 1.33e+00 3.170105230e+03 3.170106213e+03 9.0e-09 0.67
19 8.0e-09 2.5e-09 7.4e-11 1.16e+00 3.170027167e+03 3.170027387e+03 2.5e-09 0.69
20 3.3e-09 1.0e-09 1.8e-11 1.16e+00 3.170010515e+03 3.170010592e+03 1.0e-09 0.73
21 2.3e-09 7.2e-10 9.9e-12 1.28e+00 3.170006704e+03 3.170006751e+03 7.2e-10 0.78
22 1.2e-09 3.6e-10 3.1e-12 1.27e+00 3.170002969e+03 3.170002987e+03 3.6e-10 0.81
23 6.4e-10 2.1e-10 1.2e-12 1.27e+00 3.170001542e+03 3.170001551e+03 2.1e-10 0.86
24 3.1e-10 1.0e-10 3.9e-13 1.24e+00 3.170000703e+03 3.170000707e+03 1.0e-10 0.91
25 9.1e-11 3.1e-11 5.9e-14 1.19e+00 3.170000198e+03 3.170000199e+03 3.1e-11 0.94
Optimizer terminated. Time: 1.03
Interior-point solution summary
Problem status : PRIMAL_AND_DUAL_FEASIBLE
Solution status : OPTIMAL
Primal. obj: 3.1700001978e+03 nrm: 4e+09 Viol. con: 6e-01 var: 4e+03 barvar: 0e+00
Dual. obj: 3.1700001987e+03 nrm: 3e+03 Viol. con: 0e+00 var: 5e-10 barvar: 5e-09
Optimizer summary
Optimizer - time: 1.03
Interior-point - iterations : 25 time: 0.95
Basis identification - time: 0.00
Primal - iterations : 0 time: 0.00
Dual - iterations : 0 time: 0.00
Clean primal - iterations : 0 time: 0.00
Clean dual - iterations : 0 time: 0.00
Simplex - time: 0.00
Primal simplex - iterations : 0 time: 0.00
Dual simplex - iterations : 0 time: 0.00
Mixed integer - relaxations: 0 time: 0.00
Status: Solved
Optimal value (cvx_optval): +3170