How to slove the error : Failed,NaN

1

CVX output：
Calling Mosek 9.1.9: 11251 variables, 5465 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 : 5465
Cones : 2627
Scalar variables : 11251
Matrix variables : 0
Integer variables : 0

Optimizer started.
Presolve started.
Linear dependency checker started.
Linear dependency checker terminated.
Eliminator started.
Freed constraints in eliminator : 2524
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: 0.03
Problem
Name :
Objective sense : min
Type : CONIC (conic optimization problem)
Constraints : 5465
Cones : 2627
Scalar variables : 11251
Matrix variables : 0
Integer variables : 0

Optimizer - threads : 4
Optimizer - solved problem : the primal
Optimizer - Constraints : 2420
Optimizer - Cones : 2627
Optimizer - Scalar variables : 8725 conic : 8194
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 : 1.38e+04 after factor : 2.43e+04
Factor - dense dim. : 5 flops : 6.90e+05
ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME
0 1.0e+00 1.4e+04 9.9e+05 0.00e+00 9.906075117e+05 0.000000000e+00 1.0e+00 0.06
1 2.6e-01 3.7e+03 5.1e+05 -1.00e+00 9.900324594e+05 -2.773584908e+01 2.6e-01 0.13
2 1.8e-01 2.6e+03 4.2e+05 -9.99e-01 9.898052767e+05 -4.609621745e+01 1.8e-01 0.13
3 1.6e-01 2.2e+03 3.9e+05 -9.99e-01 9.901834021e+05 -6.206103669e+01 1.6e-01 0.14
4 3.4e-02 4.7e+02 1.8e+05 -9.99e-01 9.887773562e+05 -3.360657550e+02 3.4e-02 0.14
5 8.9e-03 1.3e+02 9.3e+04 -9.98e-01 9.858710359e+05 -1.319790783e+03 8.9e-03 0.14
6 1.9e-03 2.7e+01 4.3e+04 -9.96e-01 9.755833004e+05 -6.238342435e+03 1.9e-03 0.16
7 6.6e-04 9.3e+00 2.5e+04 -9.91e-01 9.561031416e+05 -1.820960402e+04 6.6e-04 0.16
8 3.7e-04 5.2e+00 1.9e+04 -9.84e-01 9.372270619e+05 -3.235871786e+04 3.7e-04 0.17
9 1.0e-04 1.4e+00 9.5e+03 -9.79e-01 8.229868555e+05 -1.173165622e+05 1.0e-04 0.17
10 2.9e-05 4.1e-01 4.9e+03 -9.49e-01 4.831239685e+05 -3.880791516e+05 2.9e-05 0.19
11 1.0e-05 1.5e-01 2.7e+03 -8.68e-01 -2.185030233e+05 -9.625802741e+05 1.0e-05 0.19
12 4.0e-06 5.6e-02 1.3e+03 -6.81e-01 -1.416798397e+06 -1.943224870e+06 4.0e-06 0.19
13 1.1e-06 1.5e-02 3.1e+02 -2.28e-01 -2.871812604e+06 -3.074095181e+06 1.1e-06 0.20
14 3.8e-07 5.4e-03 7.5e+01 5.14e-01 -2.962358549e+06 -3.045607823e+06 3.8e-07 0.20
15 1.3e-07 1.8e-03 1.6e+01 7.13e-01 -2.229958410e+06 -2.261017037e+06 1.3e-07 0.22
16 5.9e-08 8.4e-04 5.3e+00 8.40e-01 -1.338922426e+06 -1.353700481e+06 5.9e-08 0.22
17 7.9e-09 1.1e-04 2.3e-01 9.63e-01 -2.113649631e+05 -2.134767132e+05 7.9e-09 0.22
18 2.7e-09 2.8e-05 2.9e-02 1.15e+00 -4.127728682e+04 -4.176817895e+04 2.0e-09 0.23
19 1.0e-09 1.1e-05 6.8e-03 1.06e+00 -1.110844641e+04 -1.128828742e+04 7.6e-10 0.25
20 2.0e-10 2.2e-06 6.1e-04 1.04e+00 4.259122000e+03 4.224020085e+03 1.5e-10 0.27
21 7.8e-11 8.3e-07 1.4e-04 1.05e+00 7.120599070e+03 7.107429588e+03 5.9e-11 0.28
22 7.2e-11 5.4e-07 7.5e-05 1.04e+00 7.945473887e+03 7.937000929e+03 3.8e-11 0.30
23 7.2e-11 5.4e-07 7.5e-05 1.04e+00 7.945473887e+03 7.937000929e+03 3.8e-11 0.31
24 6.9e-11 5.4e-07 7.5e-05 1.04e+00 7.945987889e+03 7.937517393e+03 3.8e-11 0.34
25 6.9e-11 5.4e-07 7.5e-05 1.03e+00 7.945987889e+03 7.937517393e+03 3.8e-11 0.36
26 6.5e-11 5.4e-07 7.5e-05 1.10e+00 7.948055888e+03 7.939595455e+03 3.8e-11 0.39
27 6.5e-11 5.4e-07 7.5e-05 1.11e+00 7.948055888e+03 7.939595455e+03 3.8e-11 0.41
28 6.5e-11 5.4e-07 7.5e-05 1.26e+00 7.948055888e+03 7.939595455e+03 3.8e-11 0.44
29 6.4e-11 5.4e-07 7.5e-05 1.01e+00 7.948287340e+03 7.939833699e+03 3.8e-11 0.45
30 6.4e-11 5.4e-07 7.4e-05 1.01e+00 7.948518759e+03 7.940071906e+03 3.8e-11 0.47
31 6.4e-11 5.4e-07 7.4e-05 1.01e+00 7.948518759e+03 7.940071906e+03 3.8e-11 0.50
Optimizer terminated. Time: 0.55

Interior-point solution summary
Problem status : UNKNOWN
Solution status : UNKNOWN
Primal. obj: 7.9485187595e+03 nrm: 6e+05 Viol. con: 1e-03 var: 0e+00 cones: 8e-06
Dual. obj: 7.9400719055e+03 nrm: 6e+06 Viol. con: 0e+00 var: 2e-01 cones: 0e+00
Optimizer summary
Optimizer - time: 0.55
Interior-point - iterations : 32 time: 0.52
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

2

The primal and dual objectives are almost equal, which is fairly good, and PRSTATUS is almost 1, which is not too bad. But the objective is rather large, which suggests that improved numerical scaling (making non-zero input data and solution be closer to one in magnitude) might help, perhaps enough for Mosek to confidently find a solution.

If you provide the complete reproducible problem, perhaps one of the Mosek experts who read the forum could say something concrete.

It looks like Mosek may have found a useful solution Unfortunately, CVX categorizes all UNKNOWN status results from Mosek as failed, and does not return any solution to the user. i think it should, but with a status indicating the UNKNOWN status of the solver. I think YALMIP does make the solution found by Mosek available to the user in such situation.

3

I get it.Thanks for your advice.

4

You can also try upgraded Mosek to the latest v9.2.