# Is that possible to obtain a larger answer using the solver mosek to maximize an object function after adding more constraints?

## I use MOSEK to maximize my function. Here is the result. Calling Mosek 9.1.9: 83006 variables, 4902 equality constraints For improved efficiency, Mosek is solving the dual problem.

MOSEK Version 9.1.9 (Build date: 2019-11-21 11:34:40)
Platform: Windows/64-X86

MOSEK warning 710: #1 (nearly) zero elements are specified in sparse col ‘’ (1225) of matrix ‘A’.
MOSEK warning 710: #1 (nearly) zero elements are specified in sparse col ‘’ (1244) of matrix ‘A’.
MOSEK warning 710: #1 (nearly) zero elements are specified in sparse col ‘’ (3026) of matrix ‘A’.
MOSEK warning 710: #1 (nearly) zero elements are specified in sparse col ‘’ (3057) of matrix ‘A’.
MOSEK warning 710: #4 (nearly) zero elements are specified in sparse col ‘’ (7082) of matrix ‘A’.
MOSEK warning 710: #5 (nearly) zero elements are specified in sparse col ‘’ (7084) of matrix ‘A’.
MOSEK warning 710: #6 (nearly) zero elements are specified in sparse col ‘’ (7096) of matrix ‘A’.
MOSEK warning 710: #7 (nearly) zero elements are specified in sparse col ‘’ (7098) of matrix ‘A’.
MOSEK warning 710: #29 (nearly) zero elements are specified in sparse col ‘’ (7114) of matrix ‘A’.
MOSEK warning 710: #7 (nearly) zero elements are specified in sparse col ‘’ (7117) of matrix ‘A’.
Warning number 710 is disabled.
Problem
Name :
Objective sense : min
Type : CONIC (conic optimization problem)
Constraints : 4902
Cones : 0
Scalar variables : 24602
Matrix variables : 92
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 : 0
Eliminator terminated.
Eliminator - tries : 2 time : 0.00
Lin. dep. - tries : 1 time : 0.01
Lin. dep. - number : 0
Presolve terminated. Time: 0.11
Problem
Name :
Objective sense : min
Type : CONIC (conic optimization problem)
Constraints : 4902
Cones : 0
Scalar variables : 24602
Matrix variables : 92
Integer variables : 0

Optimizer - solved problem : the primal
Optimizer - Constraints : 4902
Optimizer - Cones : 1
Optimizer - Scalar variables : 14565 conic : 7112
Optimizer - Semi-definite variables: 92 scalarized : 58404
Factor - setup time : 0.38 dense det. time : 0.00
Factor - ML order time : 0.06 GP order time : 0.00
Factor - nonzeros before factor : 4.95e+06 after factor : 5.88e+06
Factor - dense dim. : 2 flops : 8.73e+09
ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME
0 1.0e+00 1.7e+07 1.3e+03 0.00e+00 1.292000000e+03 0.000000000e+00 1.0e+00 0.61
1 4.2e-01 7.0e+06 8.4e+02 -1.00e+00 1.301869346e+03 -4.001241165e-03 4.2e-01 1.59
2 8.6e-02 1.4e+06 3.8e+02 -1.00e+00 1.291989178e+03 2.891663366e-02 8.6e-02 2.50
3 2.1e-02 3.6e+05 1.9e+02 -1.00e+00 1.256507267e+03 2.765749889e-01 2.1e-02 3.33
4 1.2e-02 2.0e+05 1.4e+02 -1.00e+00 1.219835468e+03 1.603252457e+00 1.2e-02 4.17
5 7.2e-03 1.2e+05 1.1e+02 -9.99e-01 1.171887681e+03 6.266038777e+00 7.2e-03 4.98
6 2.5e-03 4.2e+04 6.5e+01 -9.98e-01 9.483113883e+02 3.602691871e+01 2.5e-03 5.81
7 1.7e-03 2.8e+04 5.3e+01 -9.92e-01 7.852319715e+02 6.882045695e+01 1.7e-03 6.64
8 1.0e-03 1.7e+04 4.1e+01 -9.85e-01 4.737917326e+02 1.428949516e+02 1.0e-03 7.47
9 5.5e-04 9.2e+03 3.0e+01 -9.72e-01 -1.195692240e+02 3.134830689e+02 5.5e-04 8.27
10 4.1e-04 6.8e+03 2.5e+01 -9.42e-01 -5.372159941e+02 4.558551670e+02 4.1e-04 9.09
11 1.0e-04 1.7e+03 1.1e+01 -9.17e-01 -4.302355457e+03 1.929490256e+03 1.0e-04 10.05
12 6.8e-05 1.1e+03 8.4e+00 -6.70e-01 -5.172616643e+03 2.797391921e+03 6.8e-05 10.86
13 6.4e-05 1.1e+03 7.9e+00 -5.41e-01 -5.245498866e+03 2.944691078e+03 6.4e-05 11.67
14 3.8e-05 6.4e+02 5.2e+00 -5.20e-01 -5.628230174e+03 4.287843846e+03 3.8e-05 12.50
15 3.0e-05 5.0e+02 4.0e+00 -3.01e-01 -5.010073540e+03 5.009785132e+03 3.0e-05 13.33
16 1.3e-05 2.1e+02 1.6e+00 -1.75e-01 -1.736855066e+03 7.590836813e+03 1.3e-05 14.17
17 1.0e-05 1.7e+02 1.2e+00 2.81e-01 6.523874615e+01 8.129916233e+03 1.0e-05 14.98
18 4.6e-06 7.8e+01 4.3e-01 4.07e-01 4.850248794e+03 9.567360096e+03 4.6e-06 15.83
19 1.2e-06 2.0e+01 6.0e-02 7.16e-01 8.788237842e+03 1.015614868e+04 1.2e-06 16.78
20 4.4e-07 7.4e+00 1.4e-02 9.89e-01 9.866223379e+03 1.041511142e+04 4.4e-07 17.66
21 1.9e-07 3.2e+00 4.0e-03 1.05e+00 1.023074901e+04 1.047701834e+04 1.9e-07 18.45
22 7.2e-08 1.2e+00 9.4e-04 1.03e+00 1.034978690e+04 1.044599351e+04 7.2e-08 19.28
23 5.8e-10 9.8e-03 6.0e-07 1.02e+00 1.043351568e+04 1.043410377e+04 5.8e-10 20.23
24 4.3e-10 7.2e-03 3.8e-07 1.04e+00 1.130025121e+04 1.130069559e+04 4.3e-10 21.19
25 3.8e-10 6.3e-03 3.1e-07 1.02e+00 1.145643725e+04 1.145682961e+04 3.8e-10 22.19
26 1.7e-10 2.8e-03 9.5e-08 1.03e+00 1.250930691e+04 1.250949286e+04 1.7e-10 23.17
27 1.1e-10 1.9e-03 5.2e-08 1.01e+00 1.271644046e+04 1.271656523e+04 1.1e-10 24.14
28 1.0e-10 1.4e-03 3.6e-08 1.01e+00 1.280265856e+04 1.280275583e+04 8.6e-11 25.11
29 9.5e-11 1.4e-03 3.6e-08 9.12e-01 1.280278804e+04 1.280288527e+04 8.6e-11 26.11
30 9.5e-11 1.4e-03 3.6e-08 1.03e+00 1.280278804e+04 1.280288527e+04 8.6e-11 27.17
31 9.5e-11 1.4e-03 3.6e-08 1.03e+00 1.280278804e+04 1.280288527e+04 8.6e-11 28.20
32 9.5e-11 1.4e-03 3.6e-08 9.70e-01 1.280384525e+04 1.280394214e+04 8.6e-11 29.17
33 9.5e-11 1.4e-03 3.6e-08 9.70e-01 1.280384525e+04 1.280394214e+04 8.6e-11 30.19
34 9.5e-11 1.4e-03 3.6e-08 9.59e-01 1.280384525e+04 1.280394214e+04 8.6e-11 31.27
Optimizer terminated. Time: 32.36

Interior-point solution summary
Problem status : PRIMAL_AND_DUAL_FEASIBLE
Solution status : OPTIMAL
Primal. obj: 1.2803845249e+04 nrm: 4e+04 Viol. con: 1e-02 var: 9e+01 barvar: 0e+00
Dual. obj: 1.2803942138e+04 nrm: 2e+06 Viol. con: 0e+00 var: 2e+01 barvar: 3e-06
Optimizer summary
Optimizer - time: 32.36
Interior-point - iterations : 35 time: 32.27
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): +12804.9

## However, after I add some other linear constraints, I obtain a larger answer. Here is the result. Calling Mosek 9.1.9: 83086 variables, 4902 equality constraints For improved efficiency, Mosek is solving the dual problem.

MOSEK Version 9.1.9 (Build date: 2019-11-21 11:34:40)
Platform: Windows/64-X86

MOSEK warning 710: #1 (nearly) zero elements are specified in sparse col ‘’ (1225) of matrix ‘A’.
MOSEK warning 710: #1 (nearly) zero elements are specified in sparse col ‘’ (1244) of matrix ‘A’.
MOSEK warning 710: #1 (nearly) zero elements are specified in sparse col ‘’ (3026) of matrix ‘A’.
MOSEK warning 710: #1 (nearly) zero elements are specified in sparse col ‘’ (3057) of matrix ‘A’.
MOSEK warning 710: #4 (nearly) zero elements are specified in sparse col ‘’ (7082) of matrix ‘A’.
MOSEK warning 710: #5 (nearly) zero elements are specified in sparse col ‘’ (7084) of matrix ‘A’.
MOSEK warning 710: #6 (nearly) zero elements are specified in sparse col ‘’ (7096) of matrix ‘A’.
MOSEK warning 710: #7 (nearly) zero elements are specified in sparse col ‘’ (7098) of matrix ‘A’.
MOSEK warning 710: #29 (nearly) zero elements are specified in sparse col ‘’ (7114) of matrix ‘A’.
MOSEK warning 710: #7 (nearly) zero elements are specified in sparse col ‘’ (7117) of matrix ‘A’.
Warning number 710 is disabled.
Problem
Name :
Objective sense : min
Type : CONIC (conic optimization problem)
Constraints : 4902
Cones : 0
Scalar variables : 24682
Matrix variables : 92
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 : 0
Eliminator terminated.
Eliminator - tries : 2 time : 0.00
Lin. dep. - tries : 1 time : 0.00
Lin. dep. - number : 0
Presolve terminated. Time: 0.08
Problem
Name :
Objective sense : min
Type : CONIC (conic optimization problem)
Constraints : 4902
Cones : 0
Scalar variables : 24682
Matrix variables : 92
Integer variables : 0

Optimizer - solved problem : the primal
Optimizer - Constraints : 4902
Optimizer - Cones : 1
Optimizer - Scalar variables : 14603 conic : 7112
Optimizer - Semi-definite variables: 92 scalarized : 58404
Factor - setup time : 0.36 dense det. time : 0.00
Factor - ML order time : 0.06 GP order time : 0.00
Factor - nonzeros before factor : 4.95e+06 after factor : 5.88e+06
Factor - dense dim. : 2 flops : 8.73e+09
ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME
0 1.0e+00 1.7e+07 1.3e+03 0.00e+00 1.292000000e+03 0.000000000e+00 1.0e+00 0.56
1 4.2e-01 7.0e+06 8.3e+02 -1.00e+00 1.285927775e+03 -1.678563528e-03 4.2e-01 1.39
2 9.3e-02 1.6e+06 3.9e+02 -1.00e+00 1.272935249e+03 2.773555803e-02 9.3e-02 2.30
3 1.9e-02 3.2e+05 1.8e+02 -1.00e+00 1.231319505e+03 3.199987618e-01 1.9e-02 3.19
4 1.3e-02 2.3e+05 1.5e+02 -1.00e+00 1.210666644e+03 1.133788952e+00 1.3e-02 3.97
5 4.6e-03 7.8e+04 8.7e+01 -1.00e+00 1.081941884e+03 1.102545544e+01 4.6e-03 4.78
6 2.2e-03 3.7e+04 6.0e+01 -9.97e-01 8.848075504e+02 4.229377550e+01 2.2e-03 5.61
7 9.1e-04 1.5e+04 3.8e+01 -9.90e-01 3.664758219e+02 1.499671990e+02 9.1e-04 6.42
8 4.3e-04 7.3e+03 2.6e+01 -9.69e-01 -4.917036757e+02 3.920847142e+02 4.3e-04 7.20
9 2.0e-04 3.3e+03 1.7e+01 -9.25e-01 -2.092814166e+03 9.858129929e+02 2.0e-04 7.97
10 6.5e-05 1.1e+03 8.2e+00 -8.23e-01 -5.615291445e+03 2.845198976e+03 6.5e-05 8.91
11 5.1e-05 8.5e+02 6.6e+00 -5.23e-01 -5.875074684e+03 3.458664632e+03 5.1e-05 9.67
12 3.1e-05 5.1e+02 4.2e+00 -4.27e-01 -5.598383269e+03 4.842235142e+03 3.1e-05 10.47
13 1.1e-05 1.8e+02 1.4e+00 -1.88e-01 -1.621275509e+03 7.966606761e+03 1.1e-05 11.30
14 7.5e-06 1.3e+02 8.5e-01 3.80e-01 1.228978792e+03 8.680340296e+03 7.5e-06 12.09
15 3.0e-06 5.1e+01 2.4e-01 5.44e-01 6.331508202e+03 9.870239376e+03 3.0e-06 12.97
16 1.5e-06 2.6e+01 8.6e-02 8.60e-01 8.194159576e+03 1.005202845e+04 1.5e-06 13.75
17 4.5e-07 7.6e+00 1.5e-02 9.48e-01 9.819247469e+03 1.042217248e+04 4.5e-07 14.59
18 7.4e-08 1.2e+00 1.0e-03 1.04e+00 1.043301394e+04 1.054699964e+04 7.4e-08 15.48
19 3.9e-09 6.5e-02 1.2e-05 1.03e+00 1.046100888e+04 1.046641983e+04 3.9e-09 16.39
20 2.4e-09 4.0e-02 5.8e-06 1.01e+00 1.082146640e+04 1.082483386e+04 2.4e-09 17.34
21 2.1e-09 3.5e-02 4.6e-06 1.01e+00 1.096234546e+04 1.096523792e+04 2.1e-09 18.27
22 1.1e-09 1.9e-02 1.8e-06 1.01e+00 1.154264911e+04 1.154421150e+04 1.1e-09 19.17
23 8.9e-10 1.5e-02 1.3e-06 1.01e+00 1.177180375e+04 1.177305235e+04 8.9e-10 20.08
24 3.2e-10 5.3e-03 2.8e-07 1.01e+00 1.249002638e+04 1.249047115e+04 3.2e-10 20.98
25 1.2e-10 2.1e-03 6.7e-08 1.01e+00 1.286860212e+04 1.286877473e+04 1.2e-10 21.91
26 2.6e-11 4.4e-04 6.6e-09 1.00e+00 1.305340401e+04 1.305344085e+04 2.6e-11 22.81
27 2.6e-11 4.4e-04 6.5e-09 9.90e-01 1.305413762e+04 1.305417394e+04 2.6e-11 23.73
28 2.6e-11 4.3e-04 6.4e-09 9.96e-01 1.305431839e+04 1.305435459e+04 2.6e-11 24.70
29 2.6e-11 4.3e-04 6.4e-09 9.91e-01 1.305467830e+04 1.305471425e+04 2.6e-11 25.64
30 2.6e-11 4.3e-04 6.4e-09 9.90e-01 1.305472298e+04 1.305475890e+04 2.6e-11 26.58
31 2.6e-11 4.3e-04 6.3e-09 9.95e-01 1.305508007e+04 1.305511573e+04 2.6e-11 27.48
32 2.5e-11 4.3e-04 6.2e-09 9.91e-01 1.305543439e+04 1.305546981e+04 2.5e-11 28.42
33 2.5e-11 4.2e-04 6.2e-09 9.96e-01 1.305552237e+04 1.305555772e+04 2.5e-11 29.34
34 2.5e-11 4.2e-04 6.2e-09 1.00e+00 1.305552237e+04 1.305555772e+04 2.5e-11 30.34
35 2.5e-11 4.2e-04 6.2e-09 1.01e+00 1.305552237e+04 1.305555772e+04 2.5e-11 31.33
36 2.5e-11 4.1e-04 6.0e-09 9.93e-01 1.305692668e+04 1.305696106e+04 2.5e-11 32.25
37 2.5e-11 3.9e-04 5.5e-09 9.93e-01 1.305965289e+04 1.305968536e+04 2.3e-11 33.16
38 2.3e-11 3.9e-04 5.4e-09 9.94e-01 1.305997353e+04 1.306000578e+04 2.3e-11 34.09
39 2.3e-11 3.9e-04 5.4e-09 9.94e-01 1.305997353e+04 1.306000578e+04 2.3e-11 35.05
40 1.4e-11 2.2e-04 2.3e-09 9.93e-01 1.308037137e+04 1.308038938e+04 1.3e-11 35.98
41 9.6e-12 3.6e-05 1.5e-10 9.96e-01 1.310185654e+04 1.310185957e+04 2.1e-12 36.91
42 7.5e-12 2.6e-05 9.7e-11 9.99e-01 1.310293273e+04 1.310293495e+04 1.6e-12 37.81
43 6.8e-12 2.4e-05 8.5e-11 1.00e+00 1.310027750e+04 1.310027953e+04 1.4e-12 38.73
44 5.9e-12 1.3e-05 3.2e-11 1.00e+00 1.310160623e+04 1.310160730e+04 7.5e-13 39.67
45 5.9e-12 1.3e-05 3.2e-11 1.00e+00 1.310160623e+04 1.310160730e+04 7.5e-13 40.66
46 5.9e-12 1.3e-05 3.2e-11 1.00e+00 1.310160623e+04 1.310160730e+04 7.5e-13 41.61
Optimizer terminated. Time: 42.61

Interior-point solution summary
Problem status : PRIMAL_AND_DUAL_FEASIBLE
Solution status : OPTIMAL
Primal. obj: 1.3101606234e+04 nrm: 4e+04 Viol. con: 6e-02 var: 8e-01 barvar: 0e+00
Dual. obj: 1.3101607297e+04 nrm: 2e+06 Viol. con: 0e+00 var: 2e-01 barvar: 3e-08
Optimizer summary
Optimizer - time: 42.61
Interior-point - iterations : 47 time: 42.59
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): +13102.6

I think this situation do not make sense.
How do I fix it?

The first thing you so is pay attention to Mosek’s warnings, and fix your model to eliminate them. Have you looked at your model to discover non-zero input data coefficients) which are near zero? Either change the scaling, or if these coefficients should be exactly zero, make them exactly zero. Also, the optimal objective value is large, indicating not very good problem scaling.

The Mosek output, especially of the first problem, looks shaky. Perhaps Mosek is adversely affected by the issues I mentioned.

With your fixed-up model, you should (hopefully) not seeing addition of constraints improve the optimal objective value.

Sorry, I meet the same problem after avoiding all warnings. Here are the results. I get larger answer after adding more constraints.

## Calling Mosek 9.1.9: 41003 variables, 1517 equality constraints For improved efficiency, Mosek is solving the dual problem.

MOSEK Version 9.1.9 (Build date: 2019-11-21 11:34:40)
Platform: Windows/64-X86

Problem
Name :
Objective sense : min
Type : CONIC (conic optimization problem)
Constraints : 1517
Cones : 0
Scalar variables : 15201
Matrix variables : 64
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 : 1
Eliminator terminated.
Eliminator - tries : 2 time : 0.00
Lin. dep. - tries : 1 time : 0.00
Lin. dep. - number : 0
Presolve terminated. Time: 0.03
Problem
Name :
Objective sense : min
Type : CONIC (conic optimization problem)
Constraints : 1517
Cones : 0
Scalar variables : 15201
Matrix variables : 64
Integer variables : 0

Optimizer - solved problem : the primal
Optimizer - Constraints : 1516
Optimizer - Cones : 1
Optimizer - Scalar variables : 6812 conic : 814
Optimizer - Semi-definite variables: 64 scalarized : 25802
Factor - setup time : 0.08 dense det. time : 0.00
Factor - ML order time : 0.02 GP order time : 0.00
Factor - nonzeros before factor : 9.47e+05 after factor : 1.08e+06
Factor - dense dim. : 2 flops : 1.12e+09
ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME
0 1.0e+00 8.4e+06 6.8e+02 0.00e+00 6.740000000e+02 0.000000000e+00 1.0e+00 0.14
1 4.9e-01 4.1e+06 4.7e+02 -1.00e+00 6.722398772e+02 -1.315437148e-02 4.9e-01 0.45
2 1.1e-01 8.9e+05 2.2e+02 -1.00e+00 6.636122999e+02 -6.416959045e-02 1.1e-01 0.72
3 3.1e-02 2.6e+05 1.2e+02 -1.00e+00 6.412606630e+02 3.277793653e-01 3.1e-02 0.95
4 1.6e-02 1.3e+05 8.5e+01 -1.00e+00 6.124743001e+02 1.888920242e+00 1.6e-02 1.20
5 1.0e-02 8.7e+04 6.8e+01 -9.98e-01 5.830662071e+02 6.485694868e+00 1.0e-02 1.44
6 4.7e-03 4.0e+04 4.6e+01 -9.96e-01 4.885383664e+02 2.540868825e+01 4.7e-03 1.67
7 2.8e-03 2.3e+04 3.5e+01 -9.88e-01 3.784879153e+02 6.023876161e+01 2.8e-03 2.00
8 1.9e-03 1.6e+04 2.9e+01 -9.75e-01 2.577179221e+02 1.059339057e+02 1.9e-03 2.23
9 1.5e-03 1.2e+04 2.5e+01 -9.58e-01 1.627356033e+02 1.458633249e+02 1.5e-03 2.48
10 8.6e-04 7.2e+03 1.9e+01 -9.44e-01 -1.164852651e+02 2.828059854e+02 8.6e-04 2.72
11 5.8e-04 4.8e+03 1.5e+01 -8.96e-01 -3.792050867e+02 4.551906511e+02 5.8e-04 2.97
12 2.1e-04 1.8e+03 7.9e+00 -8.36e-01 -1.276437839e+03 1.249652302e+03 2.1e-04 3.22
13 1.5e-04 1.3e+03 6.0e+00 -5.79e-01 -1.338835595e+03 1.668246109e+03 1.5e-04 3.44
14 8.1e-05 6.8e+02 3.5e+00 -4.55e-01 -1.024685954e+03 2.595806211e+03 8.1e-05 3.69
15 5.3e-05 4.5e+02 2.2e+00 -1.76e-01 -2.729896275e+02 3.275326151e+03 5.3e-05 3.92
16 4.9e-05 4.1e+02 2.0e+00 3.42e-02 3.828903496e+01 3.455193827e+03 4.9e-05 4.17
17 2.0e-05 1.7e+02 7.2e-01 8.81e-02 2.258920532e+03 4.781030318e+03 2.0e-05 4.41
18 1.3e-05 1.1e+02 4.0e-01 5.09e-01 3.438076511e+03 5.290262253e+03 1.3e-05 4.64
19 1.2e-05 1.0e+02 3.5e-01 6.98e-01 3.506948350e+03 5.226224804e+03 1.2e-05 4.89
20 5.5e-06 4.6e+01 1.1e-01 7.39e-01 4.520051423e+03 5.351826765e+03 5.5e-06 5.13
21 1.4e-06 1.2e+01 1.6e-02 9.12e-01 5.375692719e+03 5.632199761e+03 1.4e-06 5.36
22 7.5e-07 6.3e+00 6.2e-03 1.01e+00 5.571202066e+03 5.710138145e+03 7.5e-07 5.59
23 3.1e-07 2.6e+00 1.6e-03 1.03e+00 5.676565624e+03 5.734859331e+03 3.1e-07 5.83
24 2.7e-08 2.3e-01 4.4e-05 1.01e+00 5.727897317e+03 5.733551001e+03 2.7e-08 6.09
25 1.4e-09 7.4e-03 2.1e-07 1.01e+00 5.970497152e+03 5.970613560e+03 8.8e-10 6.33
26 8.0e-10 4.3e-03 9.7e-08 1.02e+00 6.258293716e+03 6.258366293e+03 5.2e-10 6.61
27 5.9e-10 3.2e-03 6.2e-08 1.01e+00 6.347107159e+03 6.347162567e+03 3.8e-10 6.88
28 1.1e-10 5.9e-04 5.1e-09 1.01e+00 6.523406005e+03 6.523417312e+03 7.0e-11 7.16
29 1.0e-10 5.9e-04 5.1e-09 1.01e+00 6.523429791e+03 6.523441089e+03 7.0e-11 7.45
30 1.0e-10 5.9e-04 5.1e-09 1.00e+00 6.523429791e+03 6.523441089e+03 7.0e-11 7.75
31 1.0e-10 5.9e-04 5.1e-09 9.99e-01 6.523429791e+03 6.523441089e+03 7.0e-11 8.06
Optimizer terminated. Time: 8.50

Interior-point solution summary
Problem status : PRIMAL_AND_DUAL_FEASIBLE
Solution status : OPTIMAL
Primal. obj: 6.5234297910e+03 nrm: 1e+04 Viol. con: 3e-03 var: 1e+01 barvar: 0e+00
Dual. obj: 6.5234410892e+03 nrm: 8e+05 Viol. con: 0e+00 var: 3e+00 barvar: 1e-06
Optimizer summary
Optimizer - time: 8.50
Interior-point - iterations : 32 time: 8.36
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): +6524.44

## Calling Mosek 9.1.9: 41022 variables, 1517 equality constraints For improved efficiency, Mosek is solving the dual problem.

MOSEK Version 9.1.9 (Build date: 2019-11-21 11:34:40)
Platform: Windows/64-X86

Problem
Name :
Objective sense : min
Type : CONIC (conic optimization problem)
Constraints : 1517
Cones : 0
Scalar variables : 15220
Matrix variables : 64
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 : 1
Eliminator terminated.
Eliminator - tries : 2 time : 0.00
Lin. dep. - tries : 1 time : 0.00
Lin. dep. - number : 0
Presolve terminated. Time: 0.03
Problem
Name :
Objective sense : min
Type : CONIC (conic optimization problem)
Constraints : 1517
Cones : 0
Scalar variables : 15220
Matrix variables : 64
Integer variables : 0

Optimizer - solved problem : the primal
Optimizer - Constraints : 1516
Optimizer - Cones : 1
Optimizer - Scalar variables : 6820 conic : 814
Optimizer - Semi-definite variables: 64 scalarized : 25802
Factor - setup time : 0.08 dense det. time : 0.00
Factor - ML order time : 0.02 GP order time : 0.00
Factor - nonzeros before factor : 9.47e+05 after factor : 1.08e+06
Factor - dense dim. : 2 flops : 1.12e+09
ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME
0 1.0e+00 8.4e+06 6.8e+02 0.00e+00 6.740000000e+02 0.000000000e+00 1.0e+00 0.14
1 5.3e-01 4.4e+06 4.9e+02 -1.00e+00 6.745294516e+02 -1.233425697e-03 5.3e-01 0.45
2 1.1e-01 9.4e+05 2.3e+02 -1.00e+00 6.688625216e+02 2.452466787e-02 1.1e-01 0.72
3 2.8e-02 2.3e+05 1.1e+02 -1.00e+00 6.418159705e+02 2.790732065e-01 2.8e-02 0.95
4 1.3e-02 1.1e+05 7.8e+01 -1.00e+00 6.058859509e+02 1.969130764e+00 1.3e-02 1.22
5 5.0e-03 4.2e+04 4.7e+01 -9.99e-01 4.969842893e+02 1.537597036e+01 5.0e-03 1.47
6 1.8e-03 1.5e+04 2.8e+01 -9.92e-01 2.172639802e+02 7.328700700e+01 1.8e-03 1.72
7 1.1e-03 9.3e+03 2.2e+01 -9.69e-01 -2.308489351e+01 1.464626616e+02 1.1e-03 1.97
8 7.3e-04 6.1e+03 1.7e+01 -9.42e-01 -3.181292929e+02 2.541337820e+02 7.3e-04 2.20
9 2.4e-04 2.0e+03 9.2e+00 -9.03e-01 -1.637439999e+03 8.596181152e+02 2.4e-04 2.47
10 1.3e-04 1.1e+03 5.9e+00 -6.94e-01 -2.211215159e+03 1.519044271e+03 1.3e-04 2.70
11 1.2e-04 1.0e+03 5.5e+00 -4.92e-01 -2.225736123e+03 1.609691323e+03 1.2e-04 2.95
12 5.8e-05 4.9e+02 2.9e+00 -4.65e-01 -2.132625340e+03 2.733015972e+03 5.8e-05 3.20
13 4.2e-05 3.5e+02 2.0e+00 -1.28e-01 -1.347366727e+03 3.265296652e+03 4.2e-05 3.44
14 1.8e-05 1.5e+02 7.5e-01 5.81e-02 1.035961025e+03 4.500646338e+03 1.8e-05 3.69
15 1.4e-05 1.2e+02 5.2e-01 4.80e-01 1.941162830e+03 4.778916641e+03 1.4e-05 3.92
16 5.9e-06 4.9e+01 1.5e-01 5.90e-01 4.017072144e+03 5.451301468e+03 5.9e-06 4.19
17 4.3e-06 3.6e+01 9.9e-02 8.56e-01 4.370096281e+03 5.449289609e+03 4.3e-06 4.42
18 2.0e-06 1.6e+01 3.1e-02 9.11e-01 5.047686945e+03 5.565701587e+03 2.0e-06 4.67
19 6.3e-07 5.3e+00 5.8e-03 9.75e-01 5.549933305e+03 5.730327086e+03 6.3e-07 4.92
20 1.1e-07 9.1e-01 4.6e-04 1.03e+00 5.732486559e+03 5.770554253e+03 1.1e-07 5.17
21 3.8e-09 3.2e-02 2.9e-06 1.02e+00 5.754450396e+03 5.755676968e+03 3.8e-09 5.44
22 2.3e-09 1.9e-02 1.4e-06 1.02e+00 6.019668354e+03 6.020406433e+03 2.3e-09 5.74
23 1.9e-09 1.6e-02 9.9e-07 1.01e+00 6.109656259e+03 6.110249509e+03 1.9e-09 6.00
24 8.4e-10 7.1e-03 3.0e-07 1.01e+00 6.348975212e+03 6.349245219e+03 8.4e-10 6.27
25 3.7e-10 3.1e-03 8.6e-08 1.01e+00 6.466851232e+03 6.466968574e+03 3.7e-10 6.56
26 4.3e-11 3.6e-04 3.4e-09 1.00e+00 6.542414574e+03 6.542428273e+03 4.3e-11 6.84
27 4.2e-11 3.5e-04 3.4e-09 9.94e-01 6.542541865e+03 6.542555393e+03 4.2e-11 7.14
28 4.2e-11 3.5e-04 3.4e-09 1.00e+00 6.542549722e+03 6.542563240e+03 4.2e-11 7.45
29 4.2e-11 3.5e-04 3.4e-09 1.00e+00 6.542551684e+03 6.542565199e+03 4.2e-11 7.75
30 4.2e-11 3.5e-04 3.3e-09 1.00e+00 6.542614371e+03 6.542627801e+03 4.2e-11 8.05
31 4.2e-11 3.5e-04 3.3e-09 9.98e-01 6.542618254e+03 6.542631679e+03 4.2e-11 8.34
32 4.2e-11 3.5e-04 3.3e-09 1.01e+00 6.542626071e+03 6.542639486e+03 4.2e-11 8.67
33 4.2e-11 3.5e-04 3.3e-09 9.99e-01 6.542641590e+03 6.542654984e+03 4.2e-11 8.97
34 3.3e-11 2.8e-04 2.4e-09 9.99e-01 6.544624735e+03 6.544635461e+03 3.3e-11 9.23
35 3.3e-11 2.8e-04 2.4e-09 9.98e-01 6.544671968e+03 6.544682631e+03 3.3e-11 9.55
36 3.3e-11 2.8e-04 2.4e-09 9.92e-01 6.544673435e+03 6.544684096e+03 3.3e-11 9.84
37 3.3e-11 2.8e-04 2.4e-09 9.99e-01 6.544685154e+03 6.544695800e+03 3.3e-11 10.14
38 3.3e-11 2.8e-04 2.4e-09 9.97e-01 6.544685154e+03 6.544695800e+03 3.3e-11 10.45
39 3.3e-11 2.8e-04 2.4e-09 9.94e-01 6.544685154e+03 6.544695800e+03 3.3e-11 10.77
40 3.1e-11 2.6e-04 2.2e-09 9.98e-01 6.545059430e+03 6.545069572e+03 3.1e-11 11.06
41 2.6e-11 2.1e-04 1.6e-09 9.98e-01 6.546468006e+03 6.546476253e+03 2.6e-11 11.33
42 1.3e-11 6.4e-05 2.6e-10 9.98e-01 6.550767759e+03 6.550770219e+03 7.6e-12 11.61
43 1.3e-11 5.5e-05 2.1e-10 9.99e-01 6.550982997e+03 6.550985095e+03 6.5e-12 11.89
44 1.2e-11 5.5e-05 2.1e-10 1.00e+00 6.550980802e+03 6.550982899e+03 6.5e-12 12.17
45 1.2e-11 5.4e-05 2.1e-10 1.00e+00 6.550978605e+03 6.550980701e+03 6.5e-12 12.50
46 1.2e-11 5.4e-05 2.1e-10 1.00e+00 6.550978605e+03 6.550980701e+03 6.5e-12 12.80
47 1.0e-11 4.5e-05 1.5e-10 1.00e+00 6.549856719e+03 6.549858445e+03 5.3e-12 13.08
48 4.9e-13 2.1e-06 1.5e-12 1.00e+00 6.550972308e+03 6.550972387e+03 2.4e-13 13.34
Optimizer terminated. Time: 13.44

Interior-point solution summary
Problem status : PRIMAL_AND_DUAL_FEASIBLE
Solution status : OPTIMAL
Primal. obj: 6.5509723085e+03 nrm: 2e+04 Viol. con: 2e-04 var: 5e-02 barvar: 0e+00
Dual. obj: 6.5509723875e+03 nrm: 8e+05 Viol. con: 0e+00 var: 1e-02 barvar: 5e-09
Optimizer summary
Optimizer - time: 13.44
Interior-point - iterations : 48 time: 13.34
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): +6551.97

Could you tell me how to deal with this situation? Which answer should I believe? Those two answers both make sense for my problem.

Violations are big in the first log output and still large but smaller in the second. That would suggest that the second solution is more accurate but both problems suffer from some sort of numerical issues.

See

and

for possible further help.

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