Same problem giving different optimal values in different computers

1

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

2

I thought the MOSEK warning is giving this error. Here is another output without the warning. It seems so strange that the same problem is giving feasible and infeasible.
Output in 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

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 : 0
Eliminator terminated.
Eliminator - tries : 1 time : 0.00
Lin. dep. - tries : 1 time : 0.02
Lin. dep. - number : 0
Presolve terminated. Time: 0.17
GP based matrix reordering started.
GP based matrix reordering terminated.
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 primal
Optimizer - Constraints : 21001
Optimizer - Cones : 12
Optimizer - Scalar variables : 233113 conic : 12113
Optimizer - Semi-definite variables: 0 scalarized : 0
Factor - setup time : 1.98 dense det. time : 0.39
Factor - ML order time : 0.27 GP order time : 0.66
Factor - nonzeros before factor : 8.91e+05 after factor : 7.36e+06
Factor - dense dim. : 2987 flops : 2.81e+10
Factor - GP saved nzs : 6.64e+04 GP saved flops : 1.21e+08
ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME
0 6.9e+00 3.6e+01 3.5e+02 0.00e+00 3.489254637e+02 0.000000000e+00 1.0e+00 2.30
1 6.4e+00 3.3e+01 9.8e+01 -6.29e-01 1.846992726e+02 3.327662301e-05 9.2e-01 2.92
2 2.8e+00 1.5e+01 7.4e+01 1.87e-02 1.941068287e+02 -1.815587779e-03 4.1e-01 3.44
3 2.1e+00 1.1e+01 4.7e+01 1.97e-01 1.419960075e+02 -1.093213050e-03 3.0e-01 4.03
4 1.9e+00 1.0e+01 4.4e+01 5.69e-01 1.365394631e+02 -1.115931558e-03 2.8e-01 4.55
5 1.7e+00 8.9e+00 3.7e+01 7.68e-01 1.201482177e+02 -9.799747964e-04 2.5e-01 5.06
6 1.3e+00 6.8e+00 2.7e+01 7.62e-01 9.624322700e+01 -3.167570882e-04 1.9e-01 5.61
7 1.2e+00 6.2e+00 2.6e+01 5.26e-01 9.445553585e+01 -3.542916035e-04 1.7e-01 6.13
8 1.0e+00 5.4e+00 2.3e+01 1.74e-01 9.085006339e+01 -2.460853456e-04 1.5e-01 6.70
9 9.3e-01 4.8e+00 2.1e+01 2.02e-01 8.634355597e+01 -5.883998822e-05 1.3e-01 7.25
10 8.4e-01 4.3e+00 1.9e+01 1.74e-01 8.356599953e+01 2.370293138e-05 1.2e-01 7.78
11 7.3e-01 3.8e+00 1.7e+01 1.03e-01 8.095027308e+01 4.990182078e-05 1.1e-01 8.30
12 6.3e-01 3.2e+00 1.6e+01 -1.49e-02 7.932520991e+01 8.729902594e-05 9.1e-02 8.81
13 5.1e-01 2.6e+00 1.4e+01 -1.63e-01 7.841173300e+01 1.926614182e-04 7.3e-02 9.33
14 3.0e-01 1.6e+00 1.1e+01 -3.32e-01 7.726053230e+01 1.807588751e-04 4.4e-02 9.84
15 1.3e-01 6.6e-01 6.9e+00 -5.86e-01 7.258432423e+01 1.305433375e-04 1.8e-02 10.36
16 3.2e-02 1.6e-01 3.3e+00 -8.16e-01 6.000834329e+01 1.064842772e-04 4.6e-03 10.94
17 4.1e-03 2.1e-02 1.2e+00 -9.63e-01 2.896628927e+01 1.280385146e-04 5.9e-04 11.45
18 2.0e-04 1.0e-03 2.5e-01 -9.96e-01 -5.576064509e+02 1.459700977e-04 2.9e-05 11.98
19 3.7e-07 1.9e-06 1.0e-02 -1.00e+00 -3.182061821e+05 1.584853962e-04 5.3e-08 12.77
20 1.1e-10 1.9e-15 1.7e-02 -1.00e+00 -3.068282990e+14 1.633314861e-04 5.4e-17 13.56
Optimizer terminated. Time: 13.63

Interior-point solution summary
Problem status : DUAL_INFEASIBLE
Solution status : DUAL_INFEASIBLE_CER
Primal. obj: -1.0829028351e-01 nrm: 5e+04 Viol. con: 3e-08 var: 0e+00 cones: 0e+00
Optimizer summary
Optimizer - time: 13.63
Interior-point - iterations : 20 time: 13.61
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 for the same problem 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

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 : 0
Eliminator terminated.
Eliminator - tries : 1 time : 0.00
Lin. dep. - tries : 1 time : 0.00
Lin. dep. - number : 0
Presolve terminated. Time: 0.33
GP based matrix reordering started.
GP based matrix reordering terminated.
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 primal
Optimizer - Constraints : 21000
Optimizer - Cones : 12
Optimizer - Scalar variables : 233113 conic : 12113
Optimizer - Semi-definite variables: 0 scalarized : 0
Factor - setup time : 3.45 dense det. time : 0.72
Factor - ML order time : 0.53 GP order time : 0.80
Factor - nonzeros before factor : 8.97e+05 after factor : 7.27e+06
Factor - dense dim. : 2973 flops : 2.79e+10
Factor - GP saved nzs : 2.30e+05 GP saved flops : 3.47e+08
ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME
0 9.0e+00 3.6e+01 3.5e+02 0.00e+00 3.489254637e+02 -1.644853627e+00 1.0e+00 4.88
1 8.3e+00 3.3e+01 5.0e+02 4.08e-01 6.308641153e+02 6.454345207e+01 9.3e-01 6.31
2 4.6e+00 1.8e+01 4.9e+01 -1.14e-01 2.107759935e+02 1.501224400e+01 5.1e-01 7.51
3 3.1e+00 1.2e+01 2.8e+01 2.60e+00 6.550114584e+01 -1.491523391e+01 3.4e-01 8.83
4 2.2e+00 8.9e+00 1.7e+01 1.86e+00 2.467992597e+01 -2.291074173e+01 2.5e-01 10.06
5 2.0e+00 8.1e+00 1.3e+01 2.21e+00 5.404092382e+00 -3.226413241e+01 2.3e-01 11.34
6 1.3e+00 5.1e+00 6.2e+00 2.01e+00 -2.430144189e+01 -4.218094479e+01 1.4e-01 12.78
7 1.1e+00 4.4e+00 5.7e+00 1.21e+00 -3.047124036e+01 -4.800704830e+01 1.2e-01 14.09
8 6.7e-01 2.7e+00 2.7e+00 1.41e+00 -5.002267797e+01 -5.987414407e+01 7.5e-02 15.44
9 5.3e-01 2.1e+00 2.0e+00 2.95e-01 -4.699621762e+01 -5.537059078e+01 5.9e-02 16.64
10 4.2e-01 1.7e+00 1.4e+00 7.48e-01 -4.768243579e+01 -5.457938316e+01 4.7e-02 17.86
11 9.4e-02 3.7e-01 1.5e-01 7.96e-01 -5.402757178e+01 -5.566132560e+01 1.0e-02 19.58
12 4.4e-02 1.7e-01 5.0e-02 9.84e-01 -4.899136469e+01 -4.975491112e+01 4.9e-03 20.81
13 1.6e-02 6.4e-02 1.1e-02 1.03e+00 -4.079238653e+01 -4.106583877e+01 1.8e-03 22.19
14 1.3e-02 5.2e-02 7.9e-03 1.13e+00 -3.964751338e+01 -3.986309823e+01 1.5e-03 23.39
15 7.6e-03 3.0e-02 3.3e-03 1.16e+00 -3.785473103e+01 -3.797135459e+01 8.5e-04 24.59
16 3.3e-03 1.3e-02 9.0e-04 1.20e+00 -3.678564548e+01 -3.683217746e+01 3.6e-04 26.06
17 1.9e-03 7.6e-03 3.9e-04 1.15e+00 -3.640486864e+01 -3.643077048e+01 2.1e-04 27.31
18 1.7e-03 6.8e-03 3.3e-04 1.16e+00 -3.633351362e+01 -3.635640609e+01 1.9e-04 28.94
19 1.2e-03 4.8e-03 1.9e-04 1.16e+00 -3.619754016e+01 -3.621312440e+01 1.3e-04 30.28
20 8.0e-04 3.2e-03 1.0e-04 1.07e+00 -3.613917081e+01 -3.614959880e+01 9.0e-05 31.84
21 6.9e-04 2.7e-03 8.2e-05 1.05e+00 -3.611374820e+01 -3.612264284e+01 7.7e-05 33.42
22 2.4e-04 9.7e-04 1.7e-05 1.05e+00 -3.603261747e+01 -3.603571433e+01 2.7e-05 35.67
23 3.8e-05 1.5e-04 1.0e-06 1.01e+00 -3.600257518e+01 -3.600306264e+01 4.3e-06 37.70
24 2.0e-05 7.9e-05 3.9e-07 1.00e+00 -3.600065175e+01 -3.600090593e+01 2.2e-06 39.69
25 1.3e-05 5.2e-05 2.1e-07 1.00e+00 -3.599993572e+01 -3.600010319e+01 1.5e-06 41.61
26 2.4e-06 9.6e-06 1.6e-08 1.00e+00 -3.599891224e+01 -3.599894306e+01 2.7e-07 43.66
27 7.3e-07 2.9e-06 2.7e-09 1.00e+00 -3.599879409e+01 -3.599880340e+01 8.1e-08 45.69
28 9.4e-08 3.7e-07 1.2e-10 1.00e+00 -3.599874724e+01 -3.599874844e+01 1.0e-08 47.84
29 1.2e-08 5.3e-08 5.5e-12 1.00e+00 -3.599874191e+01 -3.599874206e+01 1.3e-09 49.70
Optimizer terminated. Time: 49.97

Interior-point solution summary
Problem status : PRIMAL_AND_DUAL_FEASIBLE
Solution status : OPTIMAL
Primal. obj: -3.5998741908e+01 nrm: 1e+03 Viol. con: 2e-06 var: 3e-06 cones: 0e+00
Dual. obj: -3.5998742059e+01 nrm: 1e+01 Viol. con: 0e+00 var: 2e-08 cones: 0e+00
Optimizer summary
Optimizer - time: 49.97
Interior-point - iterations : 29 time: 49.88
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): +35.9987

3

That would indicate the problem is borderline feasible/infeasible and therefore extermely unstable. Consider solving "x\geq 1 and x\leq 1" where both the 1 are obtained as results of some complicated computation which can give rounding errors. Then the actual approximations to 1 can render the problem either feasible or infeasible.

One solution is on 4 threads and the other on 24 so surely you will get different rounding in both optimization processes.

The optimal solution has slightly bigger violations than the infeasibility certificate.

See 8.1 and 8.2 in https://docs.mosek.com/latest/toolbox/debugging-tutorials.html

4

Thank you for your reply. From these outputs, is it possible to conclude that 4 threads is correct (as it solves the problem)? Or would it be wrong to do so?
I checked my code according to Section 8.3 in the link and removing the objective gives me feasibility. So maybe the problem lies with round off in the objective. Hence, I am asking the above question.

5

Hard for us to say. Only you can assert if you are satisfied with the solution.