Mosek returns "UNKNOWN_RESULT_STATUS" after very few iterations

chengg04 commented 4 years ago

I am solving a SDP problem with Mosek's default settings. I got "UNKNOWN_RESULT_STATUS" after 29 iterations and about 16 sec. Here is the log:

MOSEK warning 52: A numerically large lower bound value  2.6e+08 is specified for constraint '' (35).
MOSEK warning 53: A numerically large upper bound value  2.6e+08 is specified for constraint '' (35).
MOSEK warning 52: A numerically large lower bound value  2.0e+08 is specified for constraint '' (36).
MOSEK warning 53: A numerically large upper bound value  2.0e+08 is specified for constraint '' (36).
MOSEK warning 52: A numerically large lower bound value  1.6e+08 is specified for constraint '' (37).
MOSEK warning 53: A numerically large upper bound value  1.6e+08 is specified for constraint '' (37).
MOSEK warning 52: A numerically large lower bound value  1.4e+08 is specified for constraint '' (38).
MOSEK warning 53: A numerically large upper bound value  1.4e+08 is specified for constraint '' (38).
Problem
  Name                   :                 
  Objective sense        : min             
  Type                   : CONIC (conic optimization problem)
  Constraints            : 3685            
  Cones                  : 0               
  Scalar variables       : 0               
  Matrix variables       : 1               
  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 - 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            : 3685            
  Cones                  : 0               
  Scalar variables       : 0               
  Matrix variables       : 1               
  Integer variables      : 0               

Optimizer  - threads                : 4               
Optimizer  - solved problem         : the primal      
Optimizer  - Constraints            : 3685
Optimizer  - Cones                  : 0
Optimizer  - Scalar variables       : 3600              conic                  : 0               
Optimizer  - Semi-definite variables: 1                 scalarized             : 1830            
Factor     - setup time             : 0.73              dense det. time        : 0.00            
Factor     - ML order time          : 0.48              GP order time          : 0.00            
Factor     - nonzeros before factor : 6.79e+06          after factor           : 6.79e+06        
Factor     - dense dim.             : 0                 flops                  : 1.67e+10        
ITE PFEAS    DFEAS    GFEAS    PRSTATUS   POBJ              DOBJ              MU       TIME  
0   2.6e+08  1.0e+00  1.0e+00  0.00e+00   3.158279953e-03   0.000000000e+00   1.0e+00  0.73  
1   1.8e+08  7.0e-01  7.7e-01  -1.00e+00  3.066692134e-02   5.420588349e-01   7.0e-01  1.29  
2   1.1e+08  4.2e-01  6.3e-01  -1.00e+00  5.568211894e-02   1.468461190e+00   4.2e-01  1.79  
3   9.0e+07  3.5e-01  5.6e-01  -1.00e+00  6.366940618e-02   1.958246124e+00   3.5e-01  2.27  
4   7.4e+07  2.9e-01  5.4e-01  -1.00e+00  8.624179595e-02   2.547283217e+00   2.9e-01  2.73  
5   4.6e+07  1.8e-01  4.3e-01  -1.00e+00  1.531939943e-01   4.644791184e+00   1.8e-01  3.20  
6   2.7e+07  1.0e-01  2.8e-01  -1.00e+00  3.375460063e-01   9.012248256e+00   1.0e-01  3.67  
7   2.2e+07  8.6e-02  2.3e-01  -1.00e+00  3.835511691e-01   1.126437528e+01   8.6e-02  4.14  
8   1.3e+07  5.2e-02  2.6e-01  -1.00e+00  6.191194974e-01   1.861132387e+01   5.2e-02  4.62  
9   1.0e+07  3.9e-02  3.5e-01  -1.00e+00  8.084095382e-01   2.461863513e+01   3.9e-02  5.10  
10  6.2e+06  2.4e-02  1.7e-01  -1.00e+00  1.227082779e+00   4.142518553e+01   2.4e-02  5.58  
11  2.9e+06  1.1e-02  1.4e-01  -1.00e+00  2.377412913e+00   9.031100900e+01   1.1e-02  6.19  
12  1.4e+06  5.4e-03  5.0e-03  -1.00e+00  3.026733044e+00   1.867710864e+02   5.4e-03  6.74  
13  6.2e+05  2.4e-03  2.3e-03  -1.00e+00  2.524428198e+00   4.120670476e+02   2.4e-03  7.33  
14  2.8e+05  1.1e-03  5.6e-02  -1.00e+00  2.583309857e+00   9.206827850e+02   1.1e-03  7.80  
15  2.6e+05  1.0e-03  4.4e-02  -1.00e+00  2.592518176e+00   9.703725262e+02   1.0e-03  8.32  
16  2.6e+05  1.0e-03  4.3e-02  -1.00e+00  2.593581647e+00   9.798465321e+02   1.0e-03  8.84  
17  2.6e+05  1.0e-03  4.3e-02  -1.00e+00  2.593581647e+00   9.798465321e+02   1.0e-03  9.42  
18  2.6e+05  1.0e-03  6.9e-02  -1.00e+00  2.593594464e+00   9.807679685e+02   1.0e-03  9.91  
19  2.5e+05  1.0e-03  3.9e-02  -1.00e+00  2.596969965e+00   1.005571743e+03   1.0e-03  10.91 
20  2.5e+05  9.7e-04  5.9e-02  -1.00e+00  2.600361709e+00   1.034473602e+03   9.7e-04  11.55 
21  2.5e+05  9.7e-04  5.9e-02  -1.00e+00  2.600361709e+00   1.034473602e+03   9.7e-04  12.08 
22  2.4e+05  9.5e-04  1.3e-02  -1.00e+00  2.602267260e+00   1.058084658e+03   9.5e-04  12.55 
23  2.4e+05  9.5e-04  7.8e-02  -1.00e+00  2.602492191e+00   1.062866668e+03   9.5e-04  13.03 
24  2.4e+05  9.5e-04  7.8e-02  -1.00e+00  2.602492191e+00   1.062866668e+03   9.5e-04  13.52 
25  2.4e+05  9.4e-04  2.3e-02  -1.00e+00  2.601870491e+00   1.071753769e+03   9.4e-04  14.01 
26  2.2e+05  8.6e-04  6.7e-02  -1.00e+00  2.596581741e+00   1.161675485e+03   8.6e-04  14.46 
27  2.2e+05  8.4e-04  4.7e-02  -1.00e+00  2.595514730e+00   1.186290741e+03   8.4e-04  14.93 
28  2.2e+05  8.4e-04  6.1e-02  -1.00e+00  2.595507147e+00   1.185999695e+03   8.4e-04  15.39 
29  2.2e+05  8.4e-04  6.1e-02  -1.00e+00  2.595507147e+00   1.185999695e+03   8.4e-04  15.85 
Optimizer terminated. Time: 16.35   

Solution status: UNKNOWN_RESULT_STATUS

On the other hand, SCS is able to get better bounds after 10k iterations.

I am aware of issues #73 and #100. However, in my case the absolute value of PRSTATUS is 1, which should mean the problem is nice (https://github.com/JuliaOpt/Mosek.jl/issues/73#issuecomment-206934792).

I also tried to set the solver parameters to MSK_IPAR_INTPNT_MAX_ITERATIONS = 10000, MSK_DPAR_OPTIMIZER_MAX_TIME = 60, MSK_DPAR_MIO_TOL_REL_GAP = 1e-08, MSK_IPAR_BI_IGNORE_MAX_ITER = 1. But Mosek still terminates within 29 iterations.

erling-d-andersen commented 4 years ago

Changing the number iterations is almost always waste of time in a case like this.

Btw when PRSTATUS converge to -1 your problem is most likely either primal or dual infeasible. However, in this case Mosek cannot compute a valid certificate and hence report unknown. My guess is that the problem is primal infeasible.

Here are some things to try:

Remove the objective and resolve. Does it have a feasible solution? Some times it is easier to get a certificate with a 0 objective.
Reduce the size of the bounds or alternatively make them infinite. See the Mosek warnings.
Dump the problem to disk and email it to Mosek support for an inspection. See

https://docs.mosek.com/9.1/faq/faq.html

for how dump the problem to disk.

Hope it helps.

chengg04 commented 4 years ago

Thank you for this fast reply. I have tried to remove the objective, but Mosek still returns UNKNOWN_RESULT_STATUS after 20 seconds. I will try to scale my problem next, and probably dump the problem to Mosek.

I'll close this issue as it does not seem a problem in the JuMP side.

MOSEK / Mosek.jl

Mosek returns "UNKNOWN_RESULT_STATUS" after very few iterations #193