The status is failed and the value is NAN

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

After 10 iterations of what? We have no idea what problem you’re solving?

As for the failed problem, Mosek says PRIMAL ILLPOSED, which given that Mosek is solving the dual of your original problem, means that your original problem is assessed to be dual ill posed.

Both logs look like the optimizer is confused, possibly the problems are illposed, for instance borderline feasible-infeasible, unattained etc., but in the first case you are more lucky. See https://docs.mosek.com/modeling-cookbook/practical.html#avoiding-ill-posed-problems In a nicely posed problem the PRSTATUS column converges clearly to 1 or -1, but in your case it is wiggling around 0.