i use mosek solver, after ten iterations,the the status is failed and the value is NAN
Calling Mosek 9.1.9: 150 variables, 75 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 : 75
Cones : 39
Scalar variables : 150
Matrix variables : 0
Integer variables : 0
Optimizer started.
Presolve started.
Linear dependency checker started.
Linear dependency checker terminated.
Eliminator started.
Freed constraints in eliminator : 7
Eliminator terminated.
Eliminator - tries : 1 time : 0.00
Lin. dep. - tries : 1 time : 0.02
Lin. dep. - number : 0
Presolve terminated. Time: 0.02
Problem
Name :
Objective sense : min
Type : CONIC (conic optimization problem)
Constraints : 75
Cones : 39
Scalar variables : 150
Matrix variables : 0
Integer variables : 0
Optimizer - threads : 6
Optimizer - solved problem : the primal
Optimizer - Constraints : 23
Optimizer - Cones : 39
Optimizer - Scalar variables : 127 conic : 114
Optimizer - Semi-definite variables: 0 scalarized : 0
Factor - setup time : 0.00 dense det. time : 0.00
Factor - ML order time : 0.00 GP order time : 0.00
Factor - nonzeros before factor : 64 after factor : 72
Factor - dense dim. : 0 flops : 7.52e+02
ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME
0 1.0e+00 3.3e+01 3.2e+01 0.00e+00 3.050670128e+01 -6.750000015e-01 1.0e+00 0.02
1 2.9e-01 9.5e+00 1.1e+01 -5.88e-01 1.669832879e+01 -1.641437198e+00 2.9e-01 0.06
2 1.2e-01 4.1e+00 3.6e+00 1.52e-01 7.186071000e+00 -2.490962686e+00 1.2e-01 0.06
3 1.9e-02 6.2e-01 1.7e-01 7.07e-01 -1.264105365e+00 -2.856307830e+00 1.9e-02 0.06
4 3.8e-03 1.2e-01 1.2e-02 1.52e+00 -1.273235700e+00 -1.519125619e+00 3.8e-03 0.06
5 1.5e-03 4.8e-02 3.4e-03 1.03e+00 -1.179333059e+00 -1.275806761e+00 1.5e-03 0.06
6 3.6e-04 1.2e-02 4.5e-04 9.35e-01 -1.132919285e+00 -1.157562011e+00 3.6e-04 0.06
7 4.3e-05 1.4e-03 1.9e-05 9.88e-01 -1.119327096e+00 -1.122250785e+00 4.3e-05 0.06
8 2.1e-06 6.9e-05 2.0e-07 9.98e-01 -1.117625650e+00 -1.117769069e+00 2.1e-06 0.06
9 5.2e-07 1.7e-05 2.5e-08 9.94e-01 -1.117559869e+00 -1.117595016e+00 5.2e-07 0.06
10 3.4e-07 1.1e-05 1.5e-08 8.94e-01 -1.117548056e+00 -1.117572662e+00 3.4e-07 0.08
11 1.5e-07 5.0e-06 4.6e-09 9.17e-01 -1.117536282e+00 -1.117547751e+00 1.5e-07 0.08
12 9.0e-08 2.9e-06 2.5e-09 6.97e-01 -1.117527432e+00 -1.117535357e+00 9.0e-08 0.08
13 4.8e-08 1.6e-06 1.0e-09 7.63e-01 -1.117521491e+00 -1.117526107e+00 4.8e-08 0.08
14 2.2e-08 7.3e-07 5.0e-10 3.80e-01 -1.117511063e+00 -1.117514174e+00 2.2e-08 0.08
15 1.1e-08 3.7e-07 2.1e-10 4.61e-01 -1.117505061e+00 -1.117506900e+00 1.1e-08 0.08
16 3.9e-09 1.3e-07 8.5e-11 1.06e-02 -1.117490035e+00 -1.117491109e+00 3.9e-09 0.08
17 1.6e-09 5.3e-08 3.3e-11 1.64e-01 -1.117478810e+00 -1.117479339e+00 1.6e-09 0.09
18 5.9e-10 1.9e-08 1.3e-11 -2.11e-02 -1.117463639e+00 -1.117463783e+00 5.9e-10 0.09
19 2.0e-10 6.4e-09 4.8e-12 -9.69e-02 -1.117442962e+00 -1.117442765e+00 2.0e-10 0.09
20 6.0e-11 2.0e-09 1.6e-12 -5.03e-02 -1.117417169e+00 -1.117416712e+00 6.0e-11 0.11
21 2.5e-11 8.3e-10 6.4e-13 8.72e-02 -1.117399014e+00 -1.117398540e+00 2.5e-11 0.11
22 8.1e-12 2.6e-10 2.6e-13 -1.76e-01 -1.117363425e+00 -1.117362555e+00 8.1e-12 0.11
23 3.1e-12 1.0e-10 7.9e-14 2.67e-01 -1.117341810e+00 -1.117341240e+00 3.1e-12 0.11
24 1.1e-12 3.4e-11 2.8e-14 1.27e-02 -1.117312093e+00 -1.117311426e+00 1.1e-12 0.11
25 3.1e-13 1.0e-11 7.6e-15 1.51e-01 -1.117284149e+00 -1.117283591e+00 3.1e-13 0.11
26 7.3e-14 2.4e-12 1.2e-15 5.35e-01 -1.117266731e+00 -1.117266499e+00 7.3e-14 0.11
27 2.8e-14 4.6e-11 3.3e-16 5.94e-01 -1.117260507e+00 -1.117260380e+00 2.8e-14 0.11
28 2.0e-14 2.6e-10 2.1e-17 9.20e-01 -1.117256984e+00 -1.117256963e+00 4.4e-15 0.11
Optimizer terminated. Time: 0.14
Interior-point solution summary
Problem status : PRIMAL_AND_DUAL_FEASIBLE
Solution status : OPTIMAL
Primal. obj: -1.1172569838e+00 nrm: 9e+01 Viol. con: 2e-10 var: 0e+00 cones: 7e-12
Dual. obj: -1.1172569626e+00 nrm: 2e+05 Viol. con: 0e+00 var: 5e-11 cones: 0e+00
Optimizer summary
Optimizer - time: 0.14
Interior-point - iterations : 28 time: 0.13
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): +1.11726
Calling Mosek 9.1.9: 150 variables, 75 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 : 75
Cones : 39
Scalar variables : 150
Matrix variables : 0
Integer variables : 0
Optimizer started.
Presolve started.
Linear dependency checker started.
Linear dependency checker terminated.
Eliminator started.
Freed constraints in eliminator : 6
Eliminator terminated.
Eliminator - tries : 1 time : 0.00
Lin. dep. - tries : 1 time : 0.00
Lin. dep. - number : 0
Presolve terminated. Time: 0.00
Problem
Name :
Objective sense : min
Type : CONIC (conic optimization problem)
Constraints : 75
Cones : 39
Scalar variables : 150
Matrix variables : 0
Integer variables : 0
Optimizer - threads : 6
Optimizer - solved problem : the primal
Optimizer - Constraints : 22
Optimizer - Cones : 39
Optimizer - Scalar variables : 125 conic : 114
Optimizer - Semi-definite variables: 0 scalarized : 0
Factor - setup time : 0.00 dense det. time : 0.00
Factor - ML order time : 0.00 GP order time : 0.00
Factor - nonzeros before factor : 62 after factor : 70
Factor - dense dim. : 0 flops : 7.50e+02
ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME
0 2.3e+00 7.1e+00 4.0e+01 0.00e+00 3.821402427e+01 -6.750000015e-01 1.0e+00 0.01
1 4.3e-01 1.3e+00 7.3e+00 -3.12e-01 1.100993256e+01 -2.635323153e+00 1.9e-01 0.05
2 2.4e-01 7.4e-01 4.1e+00 5.41e-01 6.939424836e+00 -3.511277149e+00 1.1e-01 0.05
3 8.2e-02 2.5e-01 2.9e+00 -4.74e-01 -1.887730828e+00 -1.556272250e+01 3.6e-02 0.05
4 7.7e-03 2.4e-02 6.6e-01 -7.09e-01 -1.180450658e+02 -1.051503582e+02 3.4e-03 0.05
5 2.8e-03 8.6e-03 3.8e-01 -9.45e-01 -3.203238127e+02 -2.699635088e+02 1.2e-03 0.05
6 6.8e-04 2.1e-03 1.7e-01 -9.52e-01 -1.190737102e+03 -9.962487162e+02 3.0e-04 0.05
7 3.1e-04 9.7e-04 1.1e-01 -8.13e-01 -2.429506614e+03 -2.047295288e+03 1.4e-04 0.05
8 1.4e-04 4.4e-04 5.2e-02 -5.99e-01 -4.188669344e+03 -3.753078957e+03 6.2e-05 0.06
9 5.5e-05 1.7e-04 1.8e-02 -1.46e-01 -6.453711185e+03 -6.117018376e+03 2.4e-05 0.06
10 2.4e-05 7.3e-05 5.2e-03 4.20e-01 -7.439843247e+03 -7.281688376e+03 1.0e-05 0.06
11 5.2e-06 1.6e-05 3.9e-04 1.07e+00 -7.028195878e+03 -7.009439807e+03 2.3e-06 0.06
12 1.0e-06 3.2e-06 3.5e-05 1.12e+00 -6.749013419e+03 -6.745234358e+03 4.5e-07 0.06
13 3.1e-07 9.5e-07 6.1e-06 1.01e+00 -6.704182708e+03 -6.702899899e+03 1.3e-07 0.06
14 2.1e-07 6.5e-07 3.7e-06 9.09e-01 -6.696862179e+03 -6.695883876e+03 9.2e-08 0.06
15 1.1e-07 3.3e-07 1.4e-06 9.46e-01 -6.689149757e+03 -6.688605418e+03 4.6e-08 0.06
16 6.5e-08 2.0e-07 7.7e-07 7.48e-01 -6.684143132e+03 -6.683693613e+03 2.9e-08 0.06
17 3.1e-08 1.1e-07 2.9e-07 7.85e-01 -6.679160784e+03 -6.678880978e+03 1.3e-08 0.08
18 2.0e-08 2.0e-07 1.9e-07 3.76e-01 -6.675091443e+03 -6.674777642e+03 8.6e-09 0.08
19 1.1e-08 1.5e-07 8.3e-08 6.07e-01 -6.671713284e+03 -6.671509545e+03 4.6e-09 0.08
20 3.9e-09 9.6e-08 3.4e-08 1.01e-01 -6.664192751e+03 -6.663936735e+03 1.7e-09 0.08
21 1.5e-09 1.2e-07 1.3e-08 8.12e-02 -6.657234787e+03 -6.656982467e+03 6.6e-10 0.08
22 4.9e-10 1.0e-07 4.7e-09 -3.53e-02 -6.647070479e+03 -6.646764977e+03 2.1e-10 0.08
23 1.9e-10 3.4e-08 1.8e-09 -1.10e-02 -6.637400453e+03 -6.637074884e+03 8.1e-11 0.09
24 5.6e-11 1.6e-08 6.8e-10 -1.66e-01 -6.621071598e+03 -6.620587218e+03 2.5e-11 0.09
25 2.3e-11 7.7e-09 2.7e-10 2.41e-02 -6.608735601e+03 -6.608294413e+03 1.0e-11 0.09
26 6.9e-12 9.4e-09 1.0e-10 -2.27e-01 -6.583681854e+03 -6.582941344e+03 3.0e-12 0.09
27 2.4e-12 3.0e-09 3.7e-11 -3.91e-02 -6.560173683e+03 -6.559417694e+03 1.1e-12 0.09
28 8.3e-13 2.6e-09 1.4e-11 -1.35e-01 -6.528458809e+03 -6.527475315e+03 3.6e-13 0.09
29 2.8e-13 6.2e-09 5.5e-12 -1.53e-01 -6.489641316e+03 -6.488373227e+03 1.2e-13 0.09
30 8.4e-14 2.1e-09 1.9e-12 -1.42e-01 -6.434103677e+03 -6.432424688e+03 3.7e-14 0.11
31 3.6e-14 8.2e-09 7.8e-13 3.00e-02 -6.392153095e+03 -6.390592721e+03 1.6e-14 0.11
32 1.0e-14 6.7e-09 3.0e-13 -2.41e-01 -6.303191199e+03 -6.300470861e+03 4.5e-15 0.11
33 3.9e-15 1.8e-08 1.1e-13 2.70e-02 -6.231614896e+03 -6.229207713e+03 1.7e-15 0.11
34 1.3e-15 1.1e-08 4.1e-14 -1.51e-01 -6.125449702e+03 -6.122181237e+03 5.7e-16 0.11
35 4.1e-16 4.3e-08 1.5e-14 -1.48e-01 -5.986827645e+03 -5.982523715e+03 1.8e-16 0.11
36 1.3e-16 2.1e-08 5.0e-15 -5.51e-02 -5.826525797e+03 -5.821715555e+03 5.7e-17 0.11
37 5.0e-17 3.8e-08 2.0e-15 -2.02e-02 -5.678155023e+03 -5.673081088e+03 2.2e-17 0.11
38 1.5e-17 2.6e-08 7.2e-16 -1.51e-01 -5.437413872e+03 -5.430120011e+03 6.5e-18 0.13
39 6.5e-18 6.8e-08 2.6e-16 2.33e-01 -5.292178154e+03 -5.287067270e+03 2.9e-18 0.13
40 1.9e-18 6.9e-08 9.2e-17 -1.03e-01 -5.024658616e+03 -5.017476344e+03 8.5e-19 0.13
41 5.9e-19 2.0e-07 2.5e-17 1.35e-01 -4.788042223e+03 -4.782099997e+03 2.6e-19 0.13
Optimizer terminated. Time: 0.14
Interior-point solution summary
Problem status : ILL_POSED
Solution status : PRIMAL_ILLPOSED_CER
Dual. obj: -9.1956919652e-07 nrm: 8e+01 Viol. con: 0e+00 var: 1e-09 cones: 0e+00
Optimizer summary
Optimizer - time: 0.14
Interior-point - iterations : 41 time: 0.13
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: Failed
Optimal value (cvx_optval): NaN