Hello
I am solving an SOCP problem in cvx (MOSEK) in MATLAB. I ran the same problem in laptop and desktop. But I am getting one problem to be optimal and the other to be infeasible with the same data. Please suggest me where I am going wrong. Or is it an issue with the system? I am attaching the output:
Output from the desktop:
Calling Mosek 9.1.9: 233122 variables, 21011 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 710: #1 (nearly) zero elements are specified in sparse col ‘’ (224120) of matrix ‘A’.
MOSEK warning 710: #1 (nearly) zero elements are specified in sparse col ‘’ (224127) of matrix ‘A’.
MOSEK warning 710: #1 (nearly) zero elements are specified in sparse col ‘’ (224273) of matrix ‘A’.
MOSEK warning 710: #1 (nearly) zero elements are specified in sparse col ‘’ (224372) of matrix ‘A’.
MOSEK warning 710: #1 (nearly) zero elements are specified in sparse col ‘’ (224388) of matrix ‘A’.
MOSEK warning 710: #1 (nearly) zero elements are specified in sparse col ‘’ (224405) of matrix ‘A’.
MOSEK warning 710: #2 (nearly) zero elements are specified in sparse col ‘’ (224431) of matrix ‘A’.
MOSEK warning 710: #2 (nearly) zero elements are specified in sparse col ‘’ (224461) of matrix ‘A’.
MOSEK warning 710: #3 (nearly) zero elements are specified in sparse col ‘’ (224484) of matrix ‘A’.
MOSEK warning 710: #1 (nearly) zero elements are specified in sparse col ‘’ (224503) of matrix ‘A’.
Warning number 710 is disabled.
Problem
Name :
Objective sense : min
Type : CONIC (conic optimization problem)
Constraints : 21011
Cones : 11
Scalar variables : 233122
Matrix variables : 0
Integer variables : 0
Optimizer started.
Presolve started.
Linear dependency checker started.
Linear dependency checker terminated.
Eliminator started.
Freed constraints in eliminator : 768
Eliminator terminated.
Eliminator started.
Freed constraints in eliminator : 0
Eliminator terminated.
Eliminator - tries : 2 time : 0.00
Lin. dep. - tries : 1 time : 0.05
Lin. dep. - number : 1
Presolve terminated. Time: 0.70
Problem
Name :
Objective sense : min
Type : CONIC (conic optimization problem)
Constraints : 21011
Cones : 11
Scalar variables : 233122
Matrix variables : 0
Integer variables : 0
Optimizer - threads : 24
Optimizer - solved problem : the dual
Optimizer - Constraints : 211342
Optimizer - Cones : 11
Optimizer - Scalar variables : 231253 conic : 11011
Optimizer - Semi-definite variables: 0 scalarized : 0
Factor - setup time : 11.81 dense det. time : 3.14
Factor - ML order time : 2.33 GP order time : 0.00
Factor - nonzeros before factor : 3.95e+06 after factor : 5.51e+06
Factor - dense dim. : 9831 flops : 3.22e+11
ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME
0 1.0e+00 1.0e+00 1.0e+00 0.00e+00 0.000000000e+00 0.000000000e+00 1.0e+00 12.81
1 9.1e-01 9.1e-01 4.9e-01 -1.77e+01 -1.716594575e-01 1.051600068e-02 9.1e-01 15.73
2 4.3e-01 4.3e-01 6.0e-02 -7.17e-01 3.518167961e-02 2.137819875e-02 4.3e-01 18.52
3 3.2e-01 3.2e-01 2.6e-02 2.11e+00 2.522528126e-02 1.486716772e-02 3.2e-01 21.20
4 8.6e-02 8.6e-02 3.9e-03 1.50e+00 2.316095620e-02 2.076456254e-02 8.6e-02 24.70
5 2.4e-02 2.4e-02 1.8e-03 -3.15e-02 -8.565116343e-05 5.757172447e-04 2.4e-02 28.27
6 8.4e-03 8.4e-03 9.5e-04 -8.35e-01 -3.775649889e-03 4.431380874e-03 8.4e-03 30.94
7 6.2e-03 6.2e-03 7.6e-04 -9.33e-01 -6.274699870e-03 4.338097559e-03 6.2e-03 33.88
8 5.1e-03 5.1e-03 6.4e-04 -8.56e-01 -7.205600417e-03 4.084067611e-03 5.1e-03 36.55
9 2.8e-03 2.8e-03 3.5e-04 -7.52e-01 -8.830103239e-03 4.143188234e-03 2.8e-03 39.80
10 2.6e-03 2.6e-03 2.9e-04 1.26e-01 -7.799500826e-03 2.217308198e-03 2.6e-03 42.53
11 1.9e-03 1.9e-03 2.1e-04 -5.52e-03 -9.241635121e-03 4.277332225e-04 1.9e-03 45.41
12 1.7e-03 1.7e-03 1.9e-04 1.00e-01 -9.278598583e-03 2.580628590e-04 1.7e-03 48.13
13 1.5e-03 1.5e-03 1.7e-04 -3.77e-03 -9.967506546e-03 4.331051283e-04 1.5e-03 51.02
14 1.4e-03 1.4e-03 1.6e-04 -1.68e-01 -1.021925316e-02 6.844150737e-04 1.4e-03 53.69
15 1.3e-03 1.3e-03 1.5e-04 -2.48e-01 -1.086199882e-02 8.711861099e-04 1.3e-03 56.34
16 1.1e-03 1.1e-03 1.4e-04 -3.27e-01 -1.166690364e-02 1.085559286e-03 1.1e-03 58.97
17 9.1e-04 9.1e-04 1.2e-04 -4.23e-01 -1.313748374e-02 1.390642184e-03 9.1e-04 61.66
18 6.8e-04 6.8e-04 9.8e-05 -5.38e-01 -1.645651712e-02 1.623381704e-03 6.8e-04 64.38
19 5.0e-04 5.0e-04 7.9e-05 -6.58e-01 -2.169061639e-02 1.460507500e-03 5.0e-04 67.05
20 3.8e-04 3.8e-04 6.6e-05 -7.49e-01 -2.596753320e-02 1.325062205e-03 3.8e-04 69.72
21 2.7e-04 2.7e-04 5.3e-05 -8.05e-01 -3.428203065e-02 1.110696431e-03 2.7e-04 72.38
22 6.2e-05 6.2e-05 2.3e-05 -8.60e-01 -1.349565724e-01 4.914485342e-04 6.2e-05 75.23
23 9.8e-06 9.8e-06 8.6e-06 -9.63e-01 -7.699843745e-01 8.319244157e-05 9.8e-06 77.89
24 5.1e-07 3.4e-07 1.5e-06 -9.94e-01 -2.086694756e+01 -1.713322716e-04 3.4e-07 81.36
25 1.7e-08 7.5e-09 2.3e-07 -9.99e-01 -9.105022096e+02 -1.721098452e-04 7.6e-09 84.89
26 2.7e-10 5.5e-12 6.2e-09 -1.00e+00 -1.216527596e+06 -2.029860750e-04 5.7e-12 88.42
27 3.6e-10 2.7e-15 1.5e-09 -1.00e+00 -2.491377913e+09 -2.029856948e-04 2.8e-15 91.94
28 4.7e-11 1.6e-22 7.4e-10 -1.00e+00 -3.524736897e-03 -7.293320693e-24 7.0e-23 95.28
Optimizer terminated. Time: 95.47
Interior-point solution summary
Problem status : DUAL_INFEASIBLE
Solution status : DUAL_INFEASIBLE_CER
Primal. obj: -3.5247368965e-03 nrm: 3e+02 Viol. con: 9e-13 var: 0e+00 cones: 0e+00
Optimizer summary
Optimizer - time: 95.47
Interior-point - iterations : 28 time: 95.45
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: Infeasible
Optimal value (cvx_optval): +Inf
Output in laptop:
Calling Mosek 9.1.9: 233122 variables, 21011 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 710: #1 (nearly) zero elements are specified in sparse col ‘’ (224120) of matrix ‘A’.
MOSEK warning 710: #1 (nearly) zero elements are specified in sparse col ‘’ (224127) of matrix ‘A’.
MOSEK warning 710: #1 (nearly) zero elements are specified in sparse col ‘’ (224273) of matrix ‘A’.
MOSEK warning 710: #1 (nearly) zero elements are specified in sparse col ‘’ (224372) of matrix ‘A’.
MOSEK warning 710: #1 (nearly) zero elements are specified in sparse col ‘’ (224388) of matrix ‘A’.
MOSEK warning 710: #1 (nearly) zero elements are specified in sparse col ‘’ (224405) of matrix ‘A’.
MOSEK warning 710: #2 (nearly) zero elements are specified in sparse col ‘’ (224431) of matrix ‘A’.
MOSEK warning 710: #2 (nearly) zero elements are specified in sparse col ‘’ (224461) of matrix ‘A’.
MOSEK warning 710: #3 (nearly) zero elements are specified in sparse col ‘’ (224484) of matrix ‘A’.
MOSEK warning 710: #1 (nearly) zero elements are specified in sparse col ‘’ (224503) of matrix ‘A’.
Warning number 710 is disabled.
Problem
Name :
Objective sense : min
Type : CONIC (conic optimization problem)
Constraints : 21011
Cones : 11
Scalar variables : 233122
Matrix variables : 0
Integer variables : 0
Optimizer started.
Presolve started.
Linear dependency checker started.
Linear dependency checker terminated.
Eliminator started.
Freed constraints in eliminator : 768
Eliminator terminated.
Eliminator started.
Freed constraints in eliminator : 0
Eliminator terminated.
Eliminator - tries : 2 time : 0.00
Lin. dep. - tries : 1 time : 0.13
Lin. dep. - number : 1
Presolve terminated. Time: 1.47
Problem
Name :
Objective sense : min
Type : CONIC (conic optimization problem)
Constraints : 21011
Cones : 11
Scalar variables : 233122
Matrix variables : 0
Integer variables : 0
Optimizer - threads : 4
Optimizer - solved problem : the dual
Optimizer - Constraints : 211342
Optimizer - Cones : 11
Optimizer - Scalar variables : 231253 conic : 11011
Optimizer - Semi-definite variables: 0 scalarized : 0
Factor - setup time : 20.92 dense det. time : 5.14
Factor - ML order time : 4.16 GP order time : 0.00
Factor - nonzeros before factor : 3.96e+06 after factor : 6.30e+06
Factor - dense dim. : 9806 flops : 3.25e+11
ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME
0 3.9e+04 1.0e+00 2.6e+00 0.00e+00 0.000000000e+00 -1.644853627e+00 1.0e+00 22.97
1 3.5e+04 8.9e-01 2.5e+00 -1.02e+00 7.063992412e-01 -8.162692294e-01 8.9e-01 33.39
2 1.1e+04 2.8e-01 1.4e+00 -9.91e-01 1.611492191e+01 1.699765528e+01 2.8e-01 45.64
3 4.9e+03 1.3e-01 9.4e-01 -1.02e+00 2.545336561e+01 3.064511155e+01 1.3e-01 55.58
4 2.6e+03 6.7e-02 6.9e-01 -1.02e+00 4.277307467e+01 5.500925385e+01 6.7e-02 65.00
5 1.2e+03 3.0e-02 4.6e-01 -1.01e+00 9.078417648e+01 1.216190815e+02 3.0e-02 74.72
6 5.0e+02 1.3e-02 2.8e-01 -9.43e-01 1.836405794e+02 2.475248654e+02 1.3e-02 83.77
7 1.7e+02 4.4e-03 1.0e-01 -6.09e-01 3.048494176e+02 3.761538006e+02 4.4e-03 94.17
8 1.4e+02 3.6e-03 6.1e-02 1.10e+00 2.745054288e+02 3.138402707e+02 3.6e-03 103.42
9 1.2e+02 3.1e-03 3.6e-02 1.87e+00 2.585928856e+02 2.778971336e+02 3.1e-03 112.63
10 1.0e+02 2.6e-03 1.8e-02 2.77e+00 2.347642401e+02 2.412150968e+02 2.6e-03 121.78
11 8.8e+01 2.3e-03 9.3e-03 4.23e+00 1.711994958e+02 1.735065156e+02 2.3e-03 131.31
12 7.1e+01 1.8e-03 3.5e-03 4.59e+00 6.684534708e+01 6.734850595e+01 1.8e-03 140.92
13 6.5e+01 1.7e-03 2.5e-03 4.60e+00 3.755808863e+01 3.785013101e+01 1.7e-03 150.31
14 6.1e+01 1.6e-03 1.9e-03 4.35e+00 2.041809057e+01 2.062083052e+01 1.6e-03 159.69
15 5.7e+01 1.5e-03 1.6e-03 3.82e+00 1.181054392e+01 1.196826602e+01 1.5e-03 174.95
16 5.6e+01 1.4e-03 1.4e-03 3.75e+00 5.202547898e+00 5.332721410e+00 1.4e-03 184.34
17 5.3e+01 1.3e-03 1.2e-03 3.62e+00 -2.106860928e+00 -2.005256898e+00 1.3e-03 193.61
18 5.0e+01 1.3e-03 1.0e-03 3.54e+00 -7.508215011e+00 -7.424865460e+00 1.3e-03 204.31
19 4.8e+01 1.2e-03 8.9e-04 3.27e+00 -1.085552652e+01 -1.078544670e+01 1.2e-03 218.55
20 4.6e+01 1.2e-03 7.9e-04 3.20e+00 -1.405936477e+01 -1.399929902e+01 1.2e-03 230.67
21 4.4e+01 1.1e-03 7.0e-04 3.08e+00 -1.686119605e+01 -1.680911740e+01 1.1e-03 243.56
22 4.2e+01 1.1e-03 6.3e-04 2.94e+00 -1.900650166e+01 -1.896105988e+01 1.1e-03 257.31
23 4.0e+01 1.0e-03 5.6e-04 2.85e+00 -2.084150769e+01 -2.080152125e+01 1.0e-03 272.69
24 3.7e+01 9.4e-04 4.7e-04 2.75e+00 -2.339652792e+01 -2.336404612e+01 9.4e-04 285.80
25 3.4e+01 8.8e-04 4.0e-04 2.52e+00 -2.508233343e+01 -2.505488267e+01 8.8e-04 295.00
26 3.3e+01 8.5e-04 3.7e-04 2.49e+00 -2.587399254e+01 -2.584870350e+01 8.5e-04 304.03
27 3.1e+01 8.0e-04 3.3e-04 2.42e+00 -2.702570746e+01 -2.700356193e+01 8.0e-04 313.16
28 2.8e+01 7.2e-04 2.6e-04 2.37e+00 -2.903988813e+01 -2.902257358e+01 7.2e-04 322.19
29 2.7e+01 6.8e-04 2.4e-04 2.22e+00 -2.966952450e+01 -2.965374582e+01 6.8e-04 332.27
30 2.5e+01 6.4e-04 2.1e-04 2.16e+00 -3.037615068e+01 -3.036223574e+01 6.4e-04 341.89
31 2.4e+01 6.1e-04 1.9e-04 2.08e+00 -3.079128144e+01 -3.077845105e+01 6.1e-04 351.36
32 2.3e+01 6.0e-04 1.8e-04 2.04e+00 -3.101404535e+01 -3.100180599e+01 6.0e-04 360.48
33 2.0e+01 5.2e-04 1.4e-04 2.01e+00 -3.193771584e+01 -3.192814735e+01 5.2e-04 369.89
34 1.8e+01 4.7e-04 1.2e-04 1.90e+00 -3.248167119e+01 -3.247351627e+01 4.7e-04 378.89
35 1.7e+01 4.4e-04 1.0e-04 1.83e+00 -3.279610094e+01 -3.278888826e+01 4.4e-04 387.81
36 1.7e+01 4.2e-04 9.6e-05 1.78e+00 -3.300741212e+01 -3.300061773e+01 4.2e-04 396.61
37 1.4e+01 3.6e-04 7.1e-05 1.75e+00 -3.361999089e+01 -3.361479474e+01 3.6e-04 406.00
38 1.4e+01 3.5e-04 6.8e-05 1.65e+00 -3.372768595e+01 -3.372270088e+01 3.5e-04 415.33
39 1.1e+01 2.7e-04 4.4e-05 1.64e+00 -3.435181014e+01 -3.434841211e+01 2.7e-04 428.61
40 1.0e+01 2.6e-04 4.0e-05 1.53e+00 -3.444603822e+01 -3.444285791e+01 2.6e-04 443.25
41 8.6e+00 2.2e-04 3.1e-05 1.51e+00 -3.470926085e+01 -3.470672355e+01 2.2e-04 458.05
42 5.2e+00 1.3e-04 1.3e-05 1.44e+00 -3.529703402e+01 -3.529580636e+01 1.3e-04 469.27
43 3.9e+00 9.9e-05 7.9e-06 1.30e+00 -3.552111052e+01 -3.552029048e+01 9.9e-05 479.69
44 3.3e+00 8.5e-05 6.1e-06 1.24e+00 -3.561411379e+01 -3.561344938e+01 8.5e-05 493.58
45 2.4e+00 6.2e-05 3.7e-06 1.22e+00 -3.574445939e+01 -3.574402652e+01 6.2e-05 503.31
46 2.4e+00 6.1e-05 3.6e-06 1.20e+00 -3.575195956e+01 -3.575153652e+01 6.1e-05 512.78
47 1.6e+00 4.0e-05 1.8e-06 1.20e+00 -3.588413860e+01 -3.588389854e+01 4.0e-05 522.30
48 9.3e-01 2.4e-05 7.5e-07 1.13e+00 -3.598867581e+01 -3.598855592e+01 2.4e-05 532.05
49 6.5e-01 1.7e-05 4.1e-07 1.09e+00 -3.603612886e+01 -3.603605526e+01 1.7e-05 541.08
50 4.6e-01 1.2e-05 2.3e-07 1.07e+00 -3.606901701e+01 -3.606897231e+01 1.2e-05 550.36
51 3.6e-01 9.1e-06 1.5e-07 1.06e+00 -3.608678899e+01 -3.608675682e+01 9.1e-06 559.39
52 3.0e-01 7.7e-06 1.2e-07 1.04e+00 -3.609725800e+01 -3.609723238e+01 7.7e-06 568.81
53 2.5e-01 6.4e-06 8.5e-08 1.04e+00 -3.610576314e+01 -3.610574347e+01 6.4e-06 577.77
54 2.9e-02 7.5e-07 1.9e-09 1.03e+00 -3.614710270e+01 -3.614710237e+01 7.5e-07 588.23
55 2.9e-02 7.4e-07 1.9e-09 1.01e+00 -3.614725269e+01 -3.614725236e+01 7.4e-07 597.36
56 2.7e-02 6.9e-07 1.7e-09 1.01e+00 -3.614755581e+01 -3.614755552e+01 6.9e-07 606.55
57 1.3e-02 3.2e-07 4.7e-10 1.01e+00 -3.615062882e+01 -3.615062878e+01 3.2e-07 616.02
58 3.4e-03 8.8e-08 5.1e-11 1.00e+00 -3.615264445e+01 -3.615264448e+01 8.8e-08 625.81
Optimizer terminated. Time: 626.34
Interior-point solution summary
Problem status : PRIMAL_AND_DUAL_FEASIBLE
Solution status : OPTIMAL
Primal. obj: -3.6152644453e+01 nrm: 1e+03 Viol. con: 2e-13 var: 2e-08 cones: 2e-08
Dual. obj: -3.6152644479e+01 nrm: 9e+01 Viol. con: 0e+00 var: 2e-04 cones: 0e+00
Optimizer summary
Optimizer - time: 626.34
Interior-point - iterations : 58 time: 626.33
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): +36.1526