# Mosek does not give the optimal value derived by simplex methods

I have a linear Polynomial Optimization problem (DSOS) programming, and I want to solve it with Mosek. Mosek first does the interior point method (IPM) and then switches to simplex method and reoptimizes it with simplex method. The acceptable answer comes from the last iteration of the simplex method. However, when I ask Julia to give me the value of the objective function, it shows me the value from the last iteration of the IPM.

Below is my script:

``````using SumOfSquares
using PermutationGroups
using DynamicPolynomials
using LinearAlgebra
using MosekTools

# Prelimiraies
a=3; b=a; r=1
mu=1; D=[0;1]*[0,1]'
@polyvar x[1:2]
@polyvar y[1:5]
fx=[(b/a)*x[2];mu*(1-a^2*x[1]^2)*x[2]-(a/b)*x[1]]
phix=(a^2*x[1]^2 +b^2*x[2]^2);

vy=monomials(y,0:1:16)

m0 = Model(Mosek.Optimizer)
PolyJuMP.setdefault!(m0, PolyJuMP.NonNegPoly, DSOSCone)
@variable m0 V0 Poly(monomials(x,0:2:18))
@variable m0 ub0
LHSUpper0= ub0- dot(gradV0, fx) - phix
@variable m0 sigma00 Poly(vy)
@variable m0 sigma10 Poly(vy)
sigmaa00=sigma00((y)=>(r-x[1],r-x[2],r+x[1],r+x[2],r^2-sum(x.^2)))
sigmaa10=sigma10((y)=>(r-x[1],r-x[2],r+x[1],r+x[2],r^2-sum(x.^2)))
@constraint m0 LHSUpper0-sigmaa00-sigmaa10*(r^2-sum(x.^2))==0
@objective m0 Min ub0
optimize!(m0)
@show value(ub0)``````

Can you show the log? I donâ€™t have Mosek so I canâ€™t test.

The following result is not for the preceding scripts because my program is too slow. However, the results are similar in the sense that Mosek only looks for the last iteration of IPM. Here the objective is â€śub4â€ť:

``````MOSEK warning 705: #1 (nearly) zero elements are specified in sparse row ''(61592) of matrix 'A'.
MOSEK warning 705: #1 (nearly) zero elements are specified in sparse row ''(61786) of matrix 'A'.
MOSEK warning 705: #1 (nearly) zero elements are specified in sparse row ''(63099) of matrix 'A'.
MOSEK warning 705: #1 (nearly) zero elements are specified in sparse row ''(63127) of matrix 'A'.
MOSEK warning 705: #1 (nearly) zero elements are specified in sparse row ''(63255) of matrix 'A'.
MOSEK warning 705: #1 (nearly) zero elements are specified in sparse row ''(63259) of matrix 'A'.
MOSEK warning 705: #1 (nearly) zero elements are specified in sparse row ''(63321) of matrix 'A'.
MOSEK warning 705: #1 (nearly) zero elements are specified in sparse row ''(64149) of matrix 'A'.
MOSEK warning 705: #2 (nearly) zero elements are specified in sparse row ''(64174) of matrix 'A'.
MOSEK warning 705: #3 (nearly) zero elements are specified in sparse row ''(64245) of matrix 'A'.
Warning number 705 is disabled.
Problem
Name                   :
Objective sense        : min
Type                   : LO (linear optimization problem)
Constraints            : 250499
Cones                  : 0
Scalar variables       : 250222
Matrix variables       : 0
Integer variables      : 0

Optimizer started.
Presolve started.
Linear dependency checker started.
Linear dependency checker terminated.
Eliminator started.
Freed constraints in eliminator : 133606
Eliminator terminated.
Eliminator started.
Freed constraints in eliminator : 6
Eliminator terminated.
Eliminator - tries                  : 2                 time                   : 0.00
Lin. dep.  - tries                  : 1                 time                   : 0.06
Lin. dep.  - number                 : 0
Presolve terminated. Time: 0.66
Problem
Name                   :
Objective sense        : min
Type                   : LO (linear optimization problem)
Constraints            : 250499
Cones                  : 0
Scalar variables       : 250222
Matrix variables       : 0
Integer variables      : 0

Optimizer  - solved problem         : the dual
Optimizer  - Constraints            : 14371
Optimizer  - Cones                  : 0
Optimizer  - Scalar variables       : 14597             conic                  : 0
Optimizer  - Semi-definite variables: 0                 scalarized             : 0
Factor     - setup time             : 0.55              dense det. time        : 0.16
Factor     - ML order time          : 0.09              GP order time          : 0.00
Factor     - nonzeros before factor : 1.21e+06          after factor           : 1.74e+06
Factor     - dense dim.             : 327               flops                  : 9.07e+08
ITE PFEAS    DFEAS    GFEAS    PRSTATUS   POBJ              DOBJ              MU       TIME
0   1.0e+02  1.1e+01  9.4e+01  0.00e+00   0.000000000e+00   1.800000000e+01   3.0e+01  1.36
1   1.1e+03  1.1e+01  9.0e+01  1.71e+00   4.684526448e-01   1.753091726e+01   2.9e+01  1.58
2   9.1e+02  8.9e+00  7.5e+01  3.16e+00   2.698346354e+00   1.246310732e+01   2.4e+01  1.78
3   8.2e+02  7.5e+00  6.4e+01  2.64e+00   3.332819177e+00   1.018644502e+01   2.1e+01  1.94
4   2.3e+02  2.1e+00  1.8e+01  2.33e+00   5.350360132e+00   6.271789764e+00   5.8e+00  2.19
5   9.9e+01  9.0e-01  7.6e+00  1.68e+00   4.906117052e+00   5.204972972e+00   2.5e+00  2.48
6   4.4e+01  4.1e-01  3.4e+00  1.45e+00   4.608106162e+00   4.723165956e+00   1.1e+00  2.67
7   2.3e+01  2.1e-01  1.8e+00  1.28e+00   4.478708228e+00   4.534840670e+00   5.8e-01  2.86
8   1.3e+01  1.1e-01  9.7e-01  1.14e+00   4.428036482e+00   4.457422304e+00   3.1e-01  3.09
9   2.9e+00  2.7e-02  2.3e-01  1.08e+00   4.357429102e+00   4.364107497e+00   7.4e-02  3.28
10  2.8e+00  2.6e-02  2.2e-01  1.06e+00   4.349376905e+00   4.355653202e+00   7.1e-02  3.45
11  7.9e-01  7.3e-03  6.2e-02  1.07e+00   4.301093960e+00   4.302774090e+00   2.0e-02  3.64
12  7.6e-01  6.9e-03  5.9e-02  9.99e-01   4.298856951e+00   4.300457652e+00   1.9e-02  3.78
13  8.8e-02  8.1e-04  6.8e-03  9.91e-01   4.270870235e+00   4.271050257e+00   2.6e-03  4.00
14  8.1e-02  7.4e-04  6.3e-03  9.30e-01   4.270115379e+00   4.270280702e+00   2.4e-03  4.17
15  3.5e-02  3.2e-04  2.7e-03  9.37e-01   4.265623399e+00   4.265695527e+00   1.0e-03  4.34
16  3.4e-02  3.1e-04  2.7e-03  9.18e-01   4.265568835e+00   4.265640624e+00   1.0e-03  4.49
17  3.3e-02  3.0e-04  2.5e-03  9.22e-01   4.265281584e+00   4.265350328e+00   9.8e-04  4.61
18  2.8e-02  2.5e-04  2.2e-03  9.24e-01   4.264471157e+00   4.264529880e+00   8.4e-04  4.77
19  1.1e-02  1.0e-04  8.9e-04  9.32e-01   4.261960082e+00   4.261984526e+00   3.7e-04  4.95
20  7.4e-03  6.8e-05  5.8e-04  9.61e-01   4.261083559e+00   4.261099577e+00   2.4e-04  5.11
21  5.9e-03  7.5e-05  4.6e-04  9.63e-01   4.260686528e+00   4.260699312e+00   1.9e-04  5.27
22  4.8e-03  1.3e-04  3.7e-04  9.67e-01   4.260335195e+00   4.260345514e+00   1.5e-04  5.44
23  4.4e-03  1.7e-04  3.4e-04  9.67e-01   4.260182951e+00   4.260192585e+00   1.5e-04  5.58
24  2.5e-03  2.5e-04  1.9e-04  9.68e-01   4.259408588e+00   4.259414000e+00   8.5e-05  5.77
25  2.0e-03  3.2e-04  1.6e-04  9.69e-01   4.259144826e+00   4.259149244e+00   6.8e-05  5.94
26  1.7e-03  3.6e-04  1.3e-04  9.71e-01   4.258922145e+00   4.258925858e+00   5.7e-05  6.11
27  1.6e-03  4.0e-04  1.2e-04  9.73e-01   4.258811658e+00   4.258815046e+00   5.2e-05  6.25
28  1.1e-03  5.3e-04  8.9e-05  9.73e-01   4.258493537e+00   4.258496054e+00   3.8e-05  6.44
29  1.0e-03  5.2e-04  7.9e-05  9.74e-01   4.258382536e+00   4.258384768e+00   3.4e-05  6.61
30  9.2e-04  5.3e-04  7.1e-05  9.75e-01   4.258290855e+00   4.258292879e+00   3.1e-05  6.77
31  8.2e-04  6.1e-04  6.3e-05  9.76e-01   4.258181173e+00   4.258182966e+00   2.7e-05  6.95
32  5.4e-04  8.6e-04  4.2e-05  9.76e-01   4.257862908e+00   4.257864098e+00   1.7e-05  7.14
33  4.6e-04  9.9e-04  3.5e-05  9.80e-01   4.257748355e+00   4.257749361e+00   1.4e-05  7.31
34  3.6e-04  1.2e-03  2.8e-05  9.81e-01   4.257597105e+00   4.257597905e+00   1.1e-05  7.53
35  2.8e-04  1.4e-03  2.1e-05  9.82e-01   4.257438207e+00   4.257438822e+00   8.7e-06  7.69
36  2.3e-04  1.6e-03  1.8e-05  9.84e-01   4.257333568e+00   4.257334076e+00   7.1e-06  7.83
37  1.8e-04  1.8e-03  1.4e-05  9.85e-01   4.257222149e+00   4.257222559e+00   5.6e-06  7.99
38  1.7e-04  1.9e-03  1.3e-05  9.87e-01   4.257175825e+00   4.257176195e+00   5.1e-06  8.14
39  1.3e-04  2.0e-03  1.0e-05  9.87e-01   4.257068245e+00   4.257068536e+00   3.9e-06  8.30
40  1.2e-04  2.1e-03  9.6e-06  9.89e-01   4.257046151e+00   4.257046427e+00   3.7e-06  8.45
41  1.2e-04  2.1e-03  9.6e-06  9.87e-01   4.257046151e+00   4.257046427e+00   3.7e-06  8.61
42  1.2e-04  2.1e-03  9.6e-06  9.57e-01   4.257046151e+00   4.257046427e+00   3.7e-06  8.81
43  1.2e-04  2.1e-03  9.6e-06  -1.19e+00  4.257046151e+00   4.257046427e+00   3.7e-06  8.92
44  1.2e-04  2.1e-03  9.6e-06  7.49e-01   4.257046151e+00   4.257046427e+00   3.7e-06  9.05
45  1.2e-04  2.1e-03  9.6e-06  9.74e-01   4.257046151e+00   4.257046427e+00   3.7e-06  9.17
46  1.2e-04  2.0e-03  9.4e-06  9.98e-01   4.257049752e+00   4.257050022e+00   3.7e-06  9.36
Basis identification started.
Primal basis identification phase started.
Primal basis identification phase terminated. Time: 0.16
Dual basis identification phase started.
Dual basis identification phase terminated. Time: 1.66
Simplex reoptimization started.
Dual simplex reoptimization started.
ITER      DEGITER(%)  PFEAS       DFEAS       POBJ                  DOBJ                  TIME
0         0.00        2.92e+03    NA          4.250812464735e+00    NA                    0.02
1121      49.38       0.00e+00    NA          4.246736222887e+00    NA                    4.58
Dual simplex reoptimization terminated. Time: 4.58
Primal simplex reoptimization started.
ITER      DEGITER(%)  PFEAS       DFEAS       POBJ                  DOBJ                  TIME
0         0.00        NA          0.00e+00    NA                    4.246736331660e+00    0.02
1         0.00        NA          0.00e+00    NA                    4.246736331659e+00    0.03
Primal simplex reoptimization terminated. Time: 0.03
Simplex reoptimization terminated. Time: 4.73
Basis identification terminated. Time: 8.89
Optimizer terminated. Time: 18.50

value(ub4) = 4.257049761318281
4.257049761318281
``````

I also added the result of my program in the following:

``````Problem
Name                   :
Objective sense        : min
Type                   : LO (linear optimization problem)
Constraints            : 1700705
Cones                  : 0
Scalar variables       : 1700193
Matrix variables       : 0
Integer variables      : 0

Optimizer started.
Presolve started.
Linear dependency checker started.
Linear dependency checker terminated.
Eliminator started.
Freed constraints in eliminator : 1657109
Eliminator terminated.
Eliminator started.
Freed constraints in eliminator : 24
Eliminator terminated.
Eliminator - tries                  : 2                 time                   : 0.00
Lin. dep.  - tries                  : 1                 time                   : 2.94
Lin. dep.  - number                 : 426
Presolve terminated. Time: 16.66
Problem
Name                   :
Objective sense        : min
Type                   : LO (linear optimization problem)
Constraints            : 1700705
Cones                  : 0
Scalar variables       : 1700193
Matrix variables       : 0
Integer variables      : 0

Optimizer  - solved problem         : the primal
Optimizer  - Constraints            : 42940
Optimizer  - Cones                  : 0
Optimizer  - Scalar variables       : 1701413           conic                  : 0
Optimizer  - Semi-definite variables: 0                 scalarized             : 0
Factor     - setup time             : 7.19              dense det. time        : 0.00
Factor     - ML order time          : 0.25              GP order time          : 0.00
Factor     - nonzeros before factor : 8.90e+06          after factor           : 1.70e+07
Factor     - dense dim.             : 2                 flops                  : 1.28e+10
ITE PFEAS    DFEAS    GFEAS    PRSTATUS   POBJ              DOBJ              MU       TIME
0   3.2e+03  1.6e+01  4.6e+04  0.00e+00   1.634937241e+04   0.000000000e+00   7.9e+00  25.86
1   3.1e+03  1.6e+01  4.5e+04  -7.24e-01  1.630379476e+04   1.448877208e-04   7.7e+00  28.34
2   3.1e+03  1.6e+01  4.4e+04  -7.78e-01  1.630130260e+04   2.384915934e-04   7.7e+00  29.75
3   3.1e+03  1.6e+01  4.4e+04  -6.91e-01  1.629771559e+04   3.607703543e-04   7.6e+00  31.14
4   3.1e+03  1.6e+01  4.4e+04  -6.75e-01  1.629319223e+04   5.140900368e-04   7.6e+00  32.73
5   3.1e+03  1.6e+01  4.4e+04  -6.85e-01  1.629262791e+04   5.333462833e-04   7.6e+00  34.06
6   3.1e+03  1.6e+01  4.4e+04  -7.28e-01  1.629250634e+04   5.377366205e-04   7.6e+00  36.69
7   3.1e+03  1.6e+01  4.4e+04  -7.93e-01  1.629250634e+04   5.377366205e-04   7.6e+00  38.94
8   3.1e+03  1.6e+01  4.4e+04  -7.93e-01  1.629250634e+04   5.377366205e-04   7.6e+00  41.41
9   3.1e+03  1.6e+01  4.4e+04  -7.93e-01  1.629250634e+04   5.377366205e-04   7.6e+00  43.47
10  3.1e+03  1.6e+01  4.4e+04  -7.95e-01  1.629250634e+04   5.377366205e-04   7.6e+00  45.56
11  3.1e+03  1.6e+01  4.4e+04  -8.10e-01  1.629250634e+04   5.377366205e-04   7.6e+00  47.69
12  3.1e+03  1.6e+01  4.4e+04  -8.85e-01  1.629240445e+04   5.438955443e-04   7.6e+00  49.83
Basis identification started.
Primal basis identification phase started.
Primal basis identification phase terminated. Time: 0.48
Dual basis identification phase started.
Dual basis identification phase terminated. Time: 0.06
Simplex reoptimization started.
Primal simplex reoptimization started.
ITER      DEGITER(%)  PFEAS       DFEAS       POBJ                  DOBJ                  TIME
0         0.00        7.62e-01    NA          2.930520743326e-02    NA                    0.19
2500      24.55       0.00e+00    NA          4.532192773164e+00    NA                    24.27
5000      12.92       0.00e+00    NA          4.271522491917e+00    NA                    35.39
5725      11.44       0.00e+00    NA          4.254961577998e+00    NA                    43.66
Primal simplex reoptimization terminated. Time: 43.66
Simplex reoptimization terminated. Time: 43.98
Basis identification terminated. Time: 66.33
Optimizer terminated. Time: 118.42

value(ub0) = 16292.404453101784
16292.404453101784``````

What is `solution_summary(model)`? Does it say anything about a warning? What version of Mosek are you using?

What is `ub4`? Please provide a fully reproducible example.

Letâ€™s forget about â€śub4â€ť. Because my program is slow, I decided to show you the result of another program with the same problem. However, now, I write the scripts and the result of my program in this comment. Sorry for the inconvenience.

Below is my code:

``````using SumOfSquares
using PermutationGroups
using DynamicPolynomials
using LinearAlgebra
using MosekTools

# Prelimiraies
a=3; b=a; r=1
mu=1; D=[0;1]*[0,1]'
@polyvar x[1:2]
@polyvar y[1:5]
fx=[(b/a)*x[2];mu*(1-a^2*x[1]^2)*x[2]-(a/b)*x[1]]
phix=(a^2*x[1]^2 +b^2*x[2]^2);
vy=monomials(y,0:1:16)

m0 = Model(Mosek.Optimizer)
PolyJuMP.setdefault!(m0, PolyJuMP.NonNegPoly, DSOSCone)
@variable m0 V0 Poly(monomials(x,0:2:18))
@variable m0 ub0
LHSUpper0= ub0- dot(gradV0, fx) - phix
@variable m0 sigma00 Poly(vy)
@variable m0 sigma10 Poly(vy)
sigmaa00=sigma00((y)=>(r-x[1],r-x[2],r+x[1],r+x[2],r^2-sum(x.^2)))
sigmaa10=sigma10((y)=>(r-x[1],r-x[2],r+x[1],r+x[2],r^2-sum(x.^2)))
@constraint m0 LHSUpper0-sigmaa00-sigmaa10*(r^2-sum(x.^2))==0
@objective m0 Min ub0
optimize!(m0)
@show value(ub0)
solution_summary(m0)
``````

And this is the result which includes ` solution_summary(m0)`:

``````Problem
Name                   :
Objective sense        : min
Type                   : LO (linear optimization problem)
Constraints            : 1700705
Cones                  : 0
Scalar variables       : 1700193
Matrix variables       : 0
Integer variables      : 0

Optimizer started.
Presolve started.
Linear dependency checker started.
Linear dependency checker terminated.
Eliminator started.
Freed constraints in eliminator : 1657109
Eliminator terminated.
Eliminator started.
Freed constraints in eliminator : 24
Eliminator terminated.
Eliminator - tries                  : 2                 time                   : 0.00
Lin. dep.  - tries                  : 1                 time                   : 2.20
Lin. dep.  - number                 : 426
Presolve terminated. Time: 12.73
Problem
Name                   :
Objective sense        : min
Type                   : LO (linear optimization problem)
Constraints            : 1700705
Cones                  : 0
Scalar variables       : 1700193
Matrix variables       : 0
Integer variables      : 0

Optimizer  - solved problem         : the primal
Optimizer  - Constraints            : 42940
Optimizer  - Cones                  : 0
Optimizer  - Scalar variables       : 1701413           conic                  : 0
Optimizer  - Semi-definite variables: 0                 scalarized             : 0
Factor     - setup time             : 5.64              dense det. time        : 0.00
Factor     - ML order time          : 0.16              GP order time          : 0.00
Factor     - nonzeros before factor : 8.90e+06          after factor           : 1.70e+07
Factor     - dense dim.             : 2                 flops                  : 1.28e+10
ITE PFEAS    DFEAS    GFEAS    PRSTATUS   POBJ              DOBJ              MU       TIME
0   3.2e+03  1.6e+01  4.6e+04  0.00e+00   1.634937241e+04   0.000000000e+00   7.9e+00  19.94
1   3.1e+03  1.6e+01  4.5e+04  -7.24e-01  1.630379476e+04   1.448877208e-04   7.7e+00  21.91
2   3.1e+03  1.6e+01  4.4e+04  -7.78e-01  1.630130260e+04   2.384915934e-04   7.7e+00  22.95
3   3.1e+03  1.6e+01  4.4e+04  -6.91e-01  1.629771559e+04   3.607703543e-04   7.6e+00  24.03
4   3.1e+03  1.6e+01  4.4e+04  -6.75e-01  1.629319223e+04   5.140900368e-04   7.6e+00  25.25
5   3.1e+03  1.6e+01  4.4e+04  -6.85e-01  1.629262791e+04   5.333462833e-04   7.6e+00  26.23
6   3.1e+03  1.6e+01  4.4e+04  -7.28e-01  1.629250634e+04   5.377366205e-04   7.6e+00  28.45
7   3.1e+03  1.6e+01  4.4e+04  -7.93e-01  1.629250634e+04   5.377366205e-04   7.6e+00  30.33
8   3.1e+03  1.6e+01  4.4e+04  -7.93e-01  1.629250634e+04   5.377366205e-04   7.6e+00  32.48
9   3.1e+03  1.6e+01  4.4e+04  -7.93e-01  1.629250634e+04   5.377366205e-04   7.6e+00  34.25
10  3.1e+03  1.6e+01  4.4e+04  -7.95e-01  1.629250634e+04   5.377366205e-04   7.6e+00  35.98
11  3.1e+03  1.6e+01  4.4e+04  -8.10e-01  1.629250634e+04   5.377366205e-04   7.6e+00  37.70
12  3.1e+03  1.6e+01  4.4e+04  -8.85e-01  1.629240445e+04   5.438955443e-04   7.6e+00  39.48
Basis identification started.
Primal basis identification phase started.
Primal basis identification phase terminated. Time: 0.47
Dual basis identification phase started.
Dual basis identification phase terminated. Time: 0.06
Simplex reoptimization started.
Primal simplex reoptimization started.
ITER      DEGITER(%)  PFEAS       DFEAS       POBJ                  DOBJ                  TIME
0         0.00        7.62e-01    NA          2.930520743326e-02    NA                    0.19
2500      24.55       0.00e+00    NA          4.532192773164e+00    NA                    21.13
5000      12.92       0.00e+00    NA          4.271522491917e+00    NA                    29.16
5725      11.44       0.00e+00    NA          4.254961577998e+00    NA                    35.23
Primal simplex reoptimization terminated. Time: 35.23
Simplex reoptimization terminated. Time: 35.53
Basis identification terminated. Time: 54.75
Optimizer terminated. Time: 95.77

value(ub0) = 16292.404453101784
* Solver : Mosek

* Status
Termination status : OPTIMAL
Primal status      : UNKNOWN_RESULT_STATUS
Dual status        : UNKNOWN_RESULT_STATUS
Message from the solver:
"Mosek.MSK_SOL_STA_UNKNOWN, Mosek.MSK_SOL_STA_OPTIMAL"

* Candidate solution
Objective value      : 1.62924e+04
Objective bound      : 1.62924e+04
Relative gap         : 0.00000e+00
Dual objective value : 5.43896e-04

* Work counters
Solve time (sec)   : 9.57660e+01
Simplex iterations : 0
Barrier iterations : 13
Node count         : 0
``````

As it can be seen, the solution is based on the last iteration of IPM but not simplex method.

Primal status : UNKNOWN_RESULT_STATUS

This suggests the Mosek knows something went wrong. You should always be cautious about accepting the results of a solver. For tricky problems, they can often fail.

I think you need to re-think your modeling approach. What are you trying to do/show? Do you need 18th order monomials?(!) Is Mosek the right choice of solver?

@blegat might have some suggestions.

Hereâ€™s the log I get with Gurobi. It says the optimal solution is `0`, so even your simplex solutions are wrong.

``````julia> optimize!(model)
Gurobi Optimizer version 9.5.1 build v9.5.1rc2 (mac64[x86])
Thread count: 4 physical cores, 8 logical processors, using up to 8 threads
Optimize a model with 1700705 rows, 1700193 columns and 12769533 nonzeros
Model fingerprint: 0x0515845a
Coefficient statistics:
Matrix range     [5e-01, 6e+06]
Objective range  [1e+00, 1e+00]
Bounds range     [0e+00, 0e+00]
RHS range        [9e+00, 9e+00]

Concurrent LP optimizer: dual simplex and barrier
Showing barrier log only...

Presolve removed 830256 rows and 890 columns (presolve time = 6s) ...
Presolve removed 830264 rows and 890 columns (presolve time = 10s) ...
Presolve removed 830382 rows and 1399 columns
Presolve time: 16.86s
Presolved: 870323 rows, 1698794 columns, 12175670 nonzeros

Ordering time: 0.75s

Barrier statistics:
Free vars  : 869992
AA' NZ     : 1.594e+07
Factor NZ  : 2.616e+07 (roughly 1.3 GB of memory)
Factor Ops : 1.582e+10 (less than 1 second per iteration)

Objective                Residual
Iter       Primal          Dual         Primal    Dual     Compl     Time
0   2.37857482e+03  0.00000000e+00  3.41e+01 6.42e+01  5.49e+00    26s
1   7.38338527e+04  0.00000000e+00  2.03e+01 4.88e+01  4.01e+00    28s
2   9.54191765e+04  0.00000000e+00  1.49e+01 4.40e+01  3.43e+00    30s
3   1.17568616e+05  0.00000000e+00  7.78e+00 2.84e+01  2.22e+00    33s
4   1.18549729e+05  0.00000000e+00  4.27e+00 2.81e+01  1.81e+00    35s
5   1.13666606e+05  0.00000000e+00  2.16e+00 2.09e+01  1.23e+00    38s
6   1.12604767e+05  0.00000000e+00  2.08e+00 1.94e+01  1.15e+00    40s
7   9.58691844e+04  0.00000000e+00  1.22e+00 1.60e+01  8.65e-01    43s
8   9.39254354e+04  0.00000000e+00  1.19e+00 1.45e+01  7.97e-01    46s
9   9.08899938e+04  0.00000000e+00  1.33e+00 1.33e+01  7.32e-01    48s
10   9.04889063e+04  0.00000000e+00  1.32e+00 1.13e+01  6.54e-01    51s
11   8.00288398e+04  0.00000000e+00  1.67e+00 9.95e+00  5.48e-01    53s
12   7.37266972e+04  0.00000000e+00  1.46e+00 9.40e+00  4.98e-01    56s
13   6.83744345e+04  0.00000000e+00  1.27e+00 8.20e+00  4.30e-01    58s
14   6.00324451e+04  0.00000000e+00  1.02e+00 6.61e+00  3.40e-01    61s
15   5.53070429e+04  0.00000000e+00  8.72e-01 5.71e+00  2.93e-01    63s
16   4.99682135e+04  0.00000000e+00  7.08e-01 4.75e+00  2.43e-01    66s
17   4.35301155e+04  0.00000000e+00  5.24e-01 4.19e+00  2.00e-01    68s
18   3.69217578e+04  0.00000000e+00  3.88e-01 3.23e+00  1.50e-01    71s
19   3.46653907e+04  0.00000000e+00  3.47e-01 2.96e+00  1.35e-01    74s
20   3.45484550e+04  0.00000000e+00  3.45e-01 2.63e+00  1.27e-01    76s
21   3.43111005e+04  0.00000000e+00  3.41e-01 2.36e+00  1.21e-01    78s
22   3.25430328e+04  0.00000000e+00  3.30e-01 2.23e+00  1.12e-01    81s
23   2.72834558e+04  0.00000000e+00  2.97e-01 1.92e+00  8.83e-02    83s
24   1.79239301e+04  0.00000000e+00  3.22e-01 1.26e+00  4.95e-02    86s
25   1.17902031e+04  0.00000000e+00  1.58e-01 6.78e-01  2.70e-02    89s
26   8.39816773e+03  0.00000000e+00  1.00e-01 5.81e-01  1.88e-02    91s
27   6.80323246e+03  0.00000000e+00  6.50e-02 3.26e-01  1.33e-02    93s
28   5.40413980e+03  0.00000000e+00  6.03e-02 2.51e-01  1.01e-02    96s
29   3.96412186e+03  0.00000000e+00  6.91e-02 1.92e-01  7.17e-03    97s
30   3.45779202e+03  0.00000000e+00  5.09e-02 1.72e-01  6.17e-03    99s
31   1.67786365e+03  0.00000000e+00  3.44e-02 6.28e-02  2.70e-03   102s
32   5.98203532e+02  0.00000000e+00  1.25e-02 3.72e-02  9.27e-04   105s
33   2.53097058e+02  0.00000000e+00  5.60e-03 2.15e-02  3.82e-04   107s
34   9.36380633e+01  0.00000000e+00  5.14e-03 1.33e-02  1.37e-04   109s
35   8.84725028e+01  0.00000000e+00  5.02e-03 1.19e-02  1.29e-04   111s
36   6.16330031e+01  0.00000000e+00  3.45e-03 5.28e-03  8.74e-05   113s
37   3.46520295e+01  0.00000000e+00  2.84e-03 3.92e-03  4.88e-05   115s
38   1.74739664e+01  0.00000000e+00  6.32e-03 1.40e-03  2.41e-05   116s
39   3.08990715e+00  0.00000000e+00  3.07e-03 8.74e-04  4.23e-06   118s
40   2.33885816e+00  0.00000000e+00  2.29e-03 2.56e-04  3.18e-06   120s
41   5.34586930e-01  0.00000000e+00  5.09e-04 9.18e-05  7.09e-07   122s
42   1.10750180e-01  0.00000000e+00  9.73e-05 1.62e-06  1.46e-07   124s
43   3.61789846e-03  0.00000000e+00  2.41e-06 1.04e-07  4.70e-09   126s
44   6.61614602e-04  0.00000000e+00  3.66e-07 8.81e-08  8.59e-10   128s
45   2.79156018e-05  0.00000000e+00  5.80e-08 7.33e-09  3.64e-11   130s
46   1.03120419e-06  0.00000000e+00  1.94e-09 1.73e-09  1.34e-12   132s
47  -1.63774210e-09  0.00000000e+00  1.67e-10 1.06e-09  1.34e-15   134s

Barrier solved model in 47 iterations and 134.08 seconds (93.50 work units)
Optimal objective -1.63774210e-09

Crossover log...

8076 DPushes remaining with DInf 0.0000000e+00               137s
356 DPushes remaining with DInf 0.0000000e+00               156s
298 DPushes remaining with DInf 0.0000000e+00               172s
292 DPushes remaining with DInf 2.1785331e+08               176s

Restart crossover...

860648 variables added to crossover basis                      181s

8082 DPushes remaining with DInf 0.0000000e+00               182s
343 DPushes remaining with DInf 0.0000000e+00               203s
321 DPushes remaining with DInf 0.0000000e+00               212s
Warning: 1 variables dropped from basis
317 DPushes remaining with DInf 3.0288211e+07               215s
Warning: 1 variables dropped from basis
Warning: 1 variables dropped from basis
292 DPushes remaining with DInf 6.4779675e+06               227s
Warning: 1 variables dropped from basis
287 DPushes remaining with DInf 2.3606628e+07               231s
257 DPushes remaining with DInf 2.3604398e+07               250s
253 DPushes remaining with DInf 2.3603731e+07               252s

106 PPushes remaining with PInf 1.7460168e+01               280s
39 PPushes remaining with PInf 1.0212502e+01               280s
0 PPushes remaining with PInf 0.0000000e+00               281s

Push phase complete: Pinf 0.0000000e+00, Dinf 7.3766851e+07    281s

Iteration    Objective       Primal Inf.    Dual Inf.      Time
7931    0.0000000e+00   0.000000e+00   7.376693e+07    281s
8007    0.0000000e+00   0.000000e+00   0.000000e+00    305s

Solved with barrier
Solved in 8007 iterations and 305.49 seconds (330.07 work units)
Optimal objective  0.000000000e+00

User-callback calls 39316, time in user-callback 0.07 sec
``````

I suppose 4.2549 from the last iteration of simplex method in Mosek is the correct answer for this optimization because Gurobi gives the same answer and also I know it from my research. I do not know why your Gurobi solved this problem that way, this is the result when I solve it by Gurobi:

``````Set parameter Username
Gurobi Optimizer version 9.5.2 build v9.5.2rc0 (win64)
Thread count: 4 physical cores, 8 logical processors, using up to 8 threads
Optimize a model with 1700705 rows, 1700193 columns and 12769533 nonzeros
Model fingerprint: 0xe058b444
Coefficient statistics:
Matrix range     [5e-01, 6e+06]
Objective range  [1e+00, 1e+00]
Bounds range     [0e+00, 0e+00]
RHS range        [9e+00, 9e+00]

Concurrent LP optimizer: dual simplex and barrier
Showing barrier log only...

Presolve removed 830264 rows and 890 columns (presolve time = 5s) ...
Presolve removed 830264 rows and 890 columns (presolve time = 10s) ...
Presolve removed 830382 rows and 1399 columns
Presolve time: 20.30s
Presolved: 870323 rows, 1698794 columns, 12175670 nonzeros

Ordering time: 1.03s

Barrier statistics:
Free vars  : 869992
AA' NZ     : 1.594e+07
Factor NZ  : 2.616e+07 (roughly 1.3 GB of memory)
Factor Ops : 1.582e+10 (roughly 1 second per iteration)

Objective                Residual
Iter       Primal          Dual         Primal    Dual     Compl     Time
0   2.37840779e+03 -1.67028920e-01  3.41e+01 6.42e+01  5.49e+00    34s
1   7.38341303e+04  1.98890081e-01  2.03e+01 4.88e+01  4.01e+00    37s
2   9.54239982e+04  3.28984795e-01  1.49e+01 4.40e+01  3.43e+00    40s
3   1.17624128e+05  1.36177972e+00  7.75e+00 2.77e+01  2.19e+00    43s
4   1.23506920e+05  1.77109501e+00  2.33e+00 2.21e+01  1.33e+00    46s
5   1.15771970e+05  1.84698504e+00  1.75e+00 1.99e+01  1.14e+00    49s
6   1.05774896e+05  1.88853545e+00  4.34e+00 1.85e+01  1.02e+00    52s
7   9.86804788e+04  2.00024679e+00  3.59e+00 1.51e+01  8.36e-01    54s
8   9.41548294e+04  2.13989546e+00  3.12e+00 1.25e+01  7.10e-01    57s
9   8.39982765e+04  2.19206369e+00  2.37e+00 1.12e+01  6.05e-01    60s
10   7.45878361e+04  2.23539708e+00  1.84e+00 1.03e+01  5.26e-01    64s
11   7.30593550e+04  2.26758379e+00  1.77e+00 9.27e+00  4.83e-01    67s
12   7.21991815e+04  2.31004131e+00  1.73e+00 8.60e+00  4.57e-01    70s
13   6.55169488e+04  2.35842593e+00  1.39e+00 8.01e+00  4.06e-01    74s
14   6.46646887e+04  2.41592242e+00  1.35e+00 7.25e+00  3.78e-01    77s
15   5.83248880e+04  2.48470072e+00  1.09e+00 6.67e+00  3.31e-01    80s
16   5.69214930e+04  2.67273038e+00  1.03e+00 5.43e+00  2.89e-01    83s
17   5.38392937e+04  2.80488664e+00  8.98e-01 4.58e+00  2.51e-01    86s
18   4.38024217e+04  2.91192505e+00  5.94e-01 3.95e+00  1.90e-01    89s
19   4.32598480e+04  2.93876632e+00  5.79e-01 3.76e+00  1.83e-01    92s
20   4.26594709e+04  3.08473809e+00  5.71e-01 2.81e+00  1.58e-01    96s
21   3.09171761e+04  3.21264260e+00  3.45e-01 1.92e+00  9.65e-02    99s
22   1.92370532e+04  3.28476559e+00  2.44e-01 1.58e+00  5.51e-02   102s
23   1.45459529e+04  3.53474423e+00  1.86e-01 6.29e-01  3.10e-02   106s
24   9.14875843e+03  3.54027129e+00  2.04e-01 5.62e-01  1.94e-02   109s
25   4.04299391e+03  3.61159825e+00  1.33e-01 2.85e-01  7.56e-03   112s
26   3.17945782e+03  3.62522330e+00  9.83e-02 2.33e-01  5.75e-03   115s
27   2.51347380e+03  3.65888202e+00  6.87e-02 1.31e-01  4.14e-03   118s
28   1.87127323e+03  3.67704081e+00  4.99e-02 8.74e-02  2.94e-03   121s
29   1.63413497e+03  3.67834759e+00  4.60e-02 8.06e-02  2.55e-03   124s
30   7.73328521e+02  3.68980516e+00  6.73e-02 3.47e-02  1.13e-03   127s
31   3.77426828e+02  3.69651752e+00  3.06e-02 1.76e-02  5.30e-04   130s
32   2.24220411e+02  3.70036016e+00  1.72e-02 1.28e-02  3.09e-04   134s
33   2.20725633e+02  3.70049056e+00  1.69e-02 1.24e-02  3.04e-04   136s
34   2.09472892e+02  3.70699094e+00  1.60e-02 9.73e-03  2.86e-04   139s
35   1.23925798e+02  3.72035047e+00  9.75e-03 5.15e-03  1.65e-04   142s
36   1.00694026e+02  3.72749677e+00  8.41e-03 3.85e-03  1.33e-04   145s
37   3.89385087e+01  3.75562852e+00  3.11e-03 2.14e-03  4.77e-05   149s
38   1.60680495e+01  3.78818828e+00  1.41e-03 1.27e-03  1.64e-05   153s
39   1.25879149e+01  3.90231510e+00  9.40e-04 6.72e-04  1.16e-05   156s
40   1.19884346e+01  3.92748853e+00  9.14e-04 5.87e-04  1.07e-05   159s
41   9.37174437e+00  3.99674366e+00  1.01e-03 3.50e-04  7.12e-06   161s
42   8.99707869e+00  4.04018916e+00  1.01e-03 2.59e-04  6.56e-06   164s
43   8.50186110e+00  4.05423017e+00  9.90e-04 2.41e-04  5.88e-06   167s
44   8.11760089e+00  4.08923231e+00  8.83e-04 2.09e-04  5.32e-06   170s
45   7.33940493e+00  4.12192976e+00  9.45e-04 1.80e-04  4.23e-06   174s
46   6.90052360e+00  4.14123119e+00  6.91e-04 1.65e-04  3.60e-06   179s
47   6.44042820e+00  4.17193813e+00  7.09e-04 1.50e-04  2.95e-06   183s
48   6.16558737e+00  4.17902643e+00  6.06e-04 1.43e-04  2.57e-06   187s
49   6.14942350e+00  4.20598525e+00  6.01e-04 1.29e-04  2.52e-06   191s
50   6.04599276e+00  4.20901941e+00  5.81e-04 1.24e-04  2.37e-06   194s
51   6.00952901e+00  4.20993247e+00  5.67e-04 1.23e-04  2.32e-06   198s
52   5.98722709e+00  4.22193663e+00  5.80e-04 1.12e-04  2.28e-06   203s
53   5.84675223e+00  4.23509427e+00  8.09e-04 1.04e-04  2.08e-06   208s
54   5.77722563e+00  4.24524982e+00  7.79e-04 9.73e-05  1.98e-06   213s
55   5.65890286e+00  4.25058980e+00  7.03e-04 8.97e-05  1.81e-06   217s
56   5.54753487e+00  4.24944578e+00  7.52e-04 8.48e-05  1.67e-06   221s
57   5.41268884e+00  4.25148349e+00  6.60e-04 7.01e-05  1.50e-06   225s
58   5.15873879e+00  4.25260301e+00  6.93e-04 5.91e-05  1.17e-06   229s
59   4.96478769e+00  4.25403026e+00  5.82e-04 4.01e-05  9.15e-07   234s
60   4.70888682e+00  4.25495293e+00  4.01e-04 2.69e-05  5.85e-07   238s
61   4.46821463e+00  4.25529162e+00  2.04e-04 1.79e-05  2.73e-07   242s
62   4.44261298e+00  4.25527802e+00  5.05e-04 1.38e-05  2.42e-07   247s
63   4.44174896e+00  4.25527838e+00  5.97e-04 1.37e-05  2.40e-07   251s
64   4.42075312e+00  4.25526979e+00  5.84e-04 1.23e-05  2.15e-07   255s
65   4.41689806e+00  4.25523911e+00  1.07e-03 1.23e-05  2.14e-07   259s
66   4.36442996e+00  4.25506559e+00  1.10e-03 8.67e-06  1.50e-07   263s
67   4.34919840e+00  4.25504084e+00  1.39e-03 7.94e-06  1.34e-07   269s
68   4.34305306e+00  4.25498214e+00  1.42e-03 7.16e-06  1.27e-07   273s
69   4.34381705e+00  4.25500046e+00  1.14e-03 7.12e-06  1.26e-07   277s
70   4.34395408e+00  4.25501301e+00  1.14e-03 7.11e-06  1.26e-07   281s
71   4.33810575e+00  4.25498950e+00  1.36e-03 7.03e-06  1.21e-07   286s
72   4.33867273e+00  4.25499677e+00  1.30e-03 7.03e-06  1.21e-07   291s
73   4.33924790e+00  4.25499991e+00  1.20e-03 7.03e-06  1.21e-07   295s
74   4.33698105e+00  4.25497971e+00  1.38e-03 6.89e-06  1.19e-07   299s
75   4.33713233e+00  4.25500191e+00  1.30e-03 6.83e-06  1.19e-07   304s
76   4.32367745e+00  4.25492090e+00  1.34e-03 6.12e-06  1.06e-07   309s
77   4.31926081e+00  4.25488383e+00  1.19e-03 3.06e-06  9.81e-08   313s
78   4.28363807e+00  4.25484688e+00  1.18e-03 2.48e-06  5.36e-08   319s
79   4.28358423e+00  4.25485065e+00  1.14e-03 3.19e-06  5.29e-08   323s
80   4.27094012e+00  4.25482285e+00  1.61e-03 2.83e-06  3.91e-08   327s
81   4.26651371e+00  4.25477304e+00  1.47e-03 1.92e-06  3.36e-08   332s
82   4.26390681e+00  4.25477090e+00  1.59e-03 1.85e-06  3.26e-08   336s
83   4.26386031e+00  4.25478345e+00  1.45e-03 1.75e-06  3.07e-08   339s
84   4.26386084e+00  4.25480563e+00  1.44e-03 2.34e-06  3.06e-08   342s
85   4.25973270e+00  4.25477727e+00  1.42e-03 2.02e-06  2.57e-08   347s
86   4.25782844e+00  4.25477559e+00  1.59e-03 2.01e-06  2.43e-08   351s
87   4.25324506e+00  4.25474647e+00  2.08e-03 9.87e-07  2.32e-08   355s
88   4.25164700e+00  4.25472656e+00  2.26e-03 9.23e-07  2.14e-08   358s
89   4.25244667e+00  4.25472981e+00  2.15e-03 5.93e-07  1.56e-08   363s
90   4.25321144e+00  4.25475443e+00  2.14e-03 6.23e-07  1.52e-08   367s
91   4.24814043e+00  4.25472332e+00  1.55e-03 4.63e-07  9.07e-09   372s
92   4.24585166e+00  4.25470240e+00  1.71e-03 4.75e-07  7.78e-09   375s
93   4.24171212e+00  4.25468670e+00  2.40e-03 4.74e-07  7.32e-09   380s
94   4.24098425e+00  4.25468684e+00  3.03e-03 4.72e-07  7.42e-09   384s
95   4.24336777e+00  4.25466015e+00  2.60e-03 4.44e-07  6.69e-09   388s
96   4.24400981e+00  4.25469275e+00  2.47e-03 4.50e-07  6.60e-09   392s
97   4.24262430e+00  4.25468964e+00  2.66e-03 4.24e-07  6.21e-09   395s
98   4.24459887e+00  4.25469368e+00  2.41e-03 4.50e-07  6.20e-09   399s
99   4.24389750e+00  4.25468451e+00  2.45e-03 4.17e-07  6.09e-09   403s
100   4.24554924e+00  4.25471269e+00  2.15e-03 3.68e-07  4.91e-09   410s
101   4.24349931e+00  4.25468436e+00  2.33e-03 3.71e-07  3.16e-09   414s
102   4.24182254e+00  4.25466078e+00  2.16e-03 6.56e-07  2.93e-09   417s
103   4.24064153e+00  4.25466188e+00  2.02e-03 6.46e-07  2.55e-09   422s
104   4.23939885e+00  4.25466385e+00  3.90e-03 1.94e-06  2.52e-09   426s
105   4.23934349e+00  4.25465444e+00  3.90e-03 1.96e-06  2.52e-09   429s
106   4.23951384e+00  4.25464289e+00  3.65e-03 1.97e-06  2.35e-09   433s
107   4.24093185e+00  4.25465460e+00  3.52e-03 1.77e-06  2.29e-09   437s
108   4.24062077e+00  4.25465183e+00  3.49e-03 1.76e-06  2.27e-09   440s
109   4.24039556e+00  4.25464771e+00  3.50e-03 1.78e-06  2.26e-09   443s
110   4.24036057e+00  4.25464051e+00  3.45e-03 1.69e-06  1.96e-09   448s
111   4.24047616e+00  4.25465294e+00  3.45e-03 1.54e-06  1.96e-09   452s
112   4.24046828e+00  4.25464954e+00  3.45e-03 1.55e-06  1.96e-09   455s
113   4.23946634e+00  4.25464597e+00  3.46e-03 1.56e-06  1.95e-09   459s
114   4.23927292e+00  4.25464484e+00  3.46e-03 1.57e-06  1.95e-09   463s
115   4.24034459e+00  4.25465880e+00  3.44e-03 1.50e-06  1.95e-09   467s
116   4.23970018e+00  4.25465720e+00  3.42e-03 1.51e-06  1.93e-09   471s
117   4.23863977e+00  4.25463453e+00  3.43e-03 1.56e-06  1.90e-09   476s
118   4.23869569e+00  4.25467512e+00  3.57e-03 1.07e-06  1.52e-09   488s
119   4.23705728e+00  4.25463625e+00  3.22e-03 1.16e-06  1.28e-09   493s
120   4.23469187e+00  4.25462746e+00  3.31e-03 1.15e-06  1.27e-09   497s
121   4.23439270e+00  4.25462742e+00  3.33e-03 1.09e-06  1.26e-09   500s
122   4.23547315e+00  4.25465316e+00  3.20e-03 9.60e-07  1.22e-09   507s
123   4.23676306e+00  4.25465585e+00  3.07e-03 9.60e-07  1.20e-09   511s
124   4.23475707e+00  4.25465661e+00  3.13e-03 9.40e-07  1.18e-09   515s
125   4.23586300e+00  4.25467690e+00  3.01e-03 8.90e-07  1.14e-09   522s
126   4.23694065e+00  4.25467022e+00  2.94e-03 8.89e-07  1.14e-09   527s
127   4.23472026e+00  4.25464817e+00  2.98e-03 9.17e-07  1.10e-09   531s
128   4.23574765e+00  4.25465968e+00  2.98e-03 8.54e-07  1.09e-09   536s
129   4.23432358e+00  4.25464940e+00  3.03e-03 8.73e-07  1.07e-09   540s
130   4.23438978e+00  4.25467185e+00  3.02e-03 7.90e-07  1.08e-09   544s
131   4.23355314e+00  4.25465341e+00  3.11e-03 8.08e-07  1.06e-09   548s
132   4.23504948e+00  4.25465809e+00  3.01e-03 7.96e-07  1.05e-09   552s
133   4.23485103e+00  4.25465484e+00  3.01e-03 7.99e-07  1.04e-09   556s
134   4.23465336e+00  4.25465303e+00  3.03e-03 8.04e-07  1.04e-09   560s
135   4.23490343e+00  4.25465505e+00  3.01e-03 7.97e-07  1.04e-09   564s

Barrier performed 135 iterations in 564.26 seconds (257.34 work units)
Sub-optimal termination - objective 4.25973270e+00

Crossover log...

8037 DPushes remaining with DInf 0.0000000e+00               569s
2129 DPushes remaining with DInf 0.0000000e+00               570s
722 DPushes remaining with DInf 0.0000000e+00               607s
642 DPushes remaining with DInf 0.0000000e+00               636s
544 DPushes remaining with DInf 0.0000000e+00               658s
535 DPushes remaining with DInf 0.0000000e+00               662s
Warning: 1 variables dropped from basis

Restart crossover...

7502 variables added to crossover basis                      667s

60526 PPushes remaining with PInf 9.8997184e-02               668s
58349 PPushes remaining with PInf 6.8845980e-02               671s
56906 PPushes remaining with PInf 5.3039611e-02               676s
51653 PPushes remaining with PInf 4.3479789e-01               680s
43782 PPushes remaining with PInf 1.0356553e+02               685s
23724 PPushes remaining with PInf 3.2789549e+01               693s
21965 PPushes remaining with PInf 1.8968886e+00               695s
17717 PPushes remaining with PInf 8.8570262e-01               700s
13469 PPushes remaining with PInf 5.7290146e-01               706s
9693 PPushes remaining with PInf 3.0275702e-01               711s
6389 PPushes remaining with PInf 1.5611568e-01               715s
2613 PPushes remaining with PInf 4.9072237e-02               721s
0 PPushes remaining with PInf 0.0000000e+00               725s

310 DPushes remaining with DInf 0.0000000e+00               726s
262 DPushes remaining with DInf 0.0000000e+00               807s

Push phase complete: Pinf 0.0000000e+00, Dinf 1.9591731e+02    891s

Iteration    Objective       Primal Inf.    Dual Inf.      Time
60571    4.2598314e+00   0.000000e+00   1.959173e+02    892s
60671    4.2531709e+00   0.000000e+00   4.084320e-03    928s
Extra simplex iterations after uncrush: 3
60740    4.2549670e+00   0.000000e+00   0.000000e+00    960s

Solved with barrier
Solved in 60740 iterations and 960.58 seconds (554.21 work units)
Optimal objective  4.254967016e+00

User-callback calls 135838, time in user-callback 0.26 sec
value(ub0) = 4.254967016250345
* Solver : Gurobi

* Status
Termination status : OPTIMAL
Primal status      : FEASIBLE_POINT
Dual status        : FEASIBLE_POINT
Message from the solver:
"Model was solved to optimality (subject to tolerances), and an optimal solution is available."

* Candidate solution
Objective value      : 4.25497e+00
Objective bound      : 4.25497e+00
Dual objective value : 4.25497e+00

* Work counters
Solve time (sec)   : 9.60960e+02
Barrier iterations : 135
Node count         : 0
``````

As it can be seen, the answer of Mosek and Gurobi are similar up to 5 digits.
The problem is not specifically related to this optimization. I think whenever Mosek switches to Simplex method, it does not consider the answer of Simplex method and only considers the answer of IPM. I am also wondering why in the solution summary of Mosek the Simplex iterations is 0 and the Barrier iterations is 13, while there are 5725 iterations for Simplex.

It looks like the optimal solution might be the second result, and weâ€™re asking for the first.

What is `value(ub0; result = 2)`?

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To install, run `] add MosekTools#odow-patch-1`, then restart Julia.

2 Likes

Thank you.
I added your patch it works perfectly. Now, I can access the desired information of optimal value.

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@Khashayar-Neshat Khyash love to see you using symmetry reduction

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