The optimization problem failed, but I can get the results of all the optimization variables

1

Successive approximation method to be employed.
For improved efficiency, SDPT3 is solving the dual problem.
SDPT3 will be called several times to refine the solution.
Original size: 7295 variables, 3661 equality constraints
196 exponentials add 1568 variables, 980 equality constraints

Cones | Errors |
Mov/Act | Centering Exp cone Poly cone | Status
--------±--------------------------------±--------
196/196 | 5.403e+00 1.762e+00 0.000e+00 | Unbounded
0/ 0 | 0.000e+00 0.000e+00 0.000e+00 | Failed
0/ 0 | 0.000e+00 0.000e+00 0.000e+00 | Failed
0/ 0 | 0.000e+00 0.000e+00 0.000e+00 | Failed

Status: Failed
Optimal value (cvx_optval): NaN

Problem
Name :
Objective sense : min
Type : CONIC (conic optimization problem)
Constraints : 4837
Cones : 2567
Scalar variables : 10431
Matrix variables : 0
Integer variables : 0

Optimizer started.
Conic interior-point optimizer started.
Presolve started.
Linear dependency checker started.
Linear dependency checker terminated.
Eliminator started.
Freed constraints in eliminator : 1449
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
Optimizer - threads : 4
Optimizer - solved problem : the primal
Optimizer - Constraints : 3187
Optimizer - Cones : 2568
Optimizer - Scalar variables : 8981 conic : 7699
Optimizer - Semi-definite variables: 0 scalarized : 0
Factor - setup time : 0.03 dense det. time : 0.00
Factor - ML order time : 0.02 GP order time : 0.00
Factor - nonzeros before factor : 1.20e+005 after factor : 2.51e+005
Factor - dense dim. : 17 flops : 6.47e+007
ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME
0 1.0e+000 5.5e+009 3.9e+009 0.00e+000 1.638400005e+016 -8.000000000e+003 1.0e+000 0.09
1 2.5e-001 1.4e+009 5.0e+008 -1.00e+000 1.638399987e+016 2.676269693e+002 2.5e-001 0.16
2 8.0e-002 4.4e+008 8.9e+007 -1.00e+000 1.638399854e+016 -1.221112330e+004 8.0e-002 0.17
3 1.3e-002 7.1e+007 5.7e+006 -1.00e+000 1.638398430e+016 -9.228276264e+004 1.3e-002 0.19
4 1.7e-003 9.3e+006 2.7e+005 -1.00e+000 1.638385953e+016 1.204391179e+004 1.7e-003 0.20
5 4.6e-004 2.6e+006 3.9e+004 -1.00e+000 1.638349990e+016 -2.729432932e+004 4.6e-004 0.22
6 1.2e-004 6.5e+005 5.0e+003 -1.00e+000 1.638188524e+016 -6.665160746e+004 1.2e-004 0.23
7 1.8e-005 1.0e+005 3.1e+002 -1.00e+000 1.636961883e+016 -8.373010384e+004 1.8e-005 0.25
8 3.1e-006 1.7e+004 2.2e+001 -9.98e-001 1.630436604e+016 -7.899456348e+004 3.1e-006 0.27
9 6.8e-007 3.8e+003 2.3e+000 -9.89e-001 1.597474525e+016 -7.851949717e+004 6.8e-007 0.28
10 1.0e-007 5.7e+002 1.5e-001 -9.50e-001 1.391688869e+016 -7.091921934e+004 1.0e-007 0.31
11 4.3e-008 2.4e+002 8.6e-002 -4.10e-001 6.974052639e+015 -3.952166802e+004 4.3e-008 0.33
12 2.2e-008 1.2e+002 2.8e-001 1.86e+000 1.981193226e+015 -1.688210761e+004 2.2e-008 0.34
13 4.6e-009 2.5e+001 8.1e-002 1.45e+000 2.838745126e+014 -9.201031345e+003 4.6e-009 0.36
14 1.5e-009 8.4e+000 5.4e-002 1.70e+000 6.659117740e+013 -8.218026810e+003 1.5e-009 0.38
15 5.8e-010 2.6e+000 4.7e-002 1.66e+000 1.387476520e+013 -7.985467734e+003 4.7e-010 0.39
16 1.2e-010 5.5e-001 2.6e-002 1.65e+000 2.090913390e+012 -7.942448100e+003 1.0e-010 0.41
17 2.2e-011 1.2e-001 1.4e-002 1.19e+000 4.213302747e+011 -7.937925182e+003 2.2e-011 0.42
18 9.5e-012 3.3e-002 7.5e-003 1.07e+000 1.100427751e+011 -7.936831208e+003 5.9e-012 0.44
19 4.8e-013 1.7e-003 1.7e-003 1.02e+000 5.538838843e+009 -7.936509004e+003 3.0e-013 0.47
20 6.2e-015 3.4e-006 7.6e-005 1.00e+000 1.126671153e+007 -7.936484126e+003 6.2e-016 0.48
21 1.6e-014 3.3e-006 7.6e-005 1.00e+000 1.109786988e+007 -7.936447047e+003 6.1e-016 0.53
22 2.0e-014 3.3e-006 7.5e-005 1.00e+000 1.093166625e+007 -7.936409387e+003 6.0e-016 0.61
23 2.7e-014 2.9e-006 7.0e-005 1.00e+000 9.622812028e+006 -7.936103389e+003 5.3e-016 0.67
24 2.6e-014 2.8e-006 7.0e-005 1.00e+000 9.587022738e+006 -7.936092489e+003 5.3e-016 0.73
25 2.7e-014 2.8e-006 7.0e-005 1.00e+000 9.578110361e+006 -7.936089753e+003 5.3e-016 0.78
26 2.7e-014 2.8e-006 7.0e-005 1.00e+000 9.573658527e+006 -7.936088384e+003 5.3e-016 0.81
27 2.7e-014 2.8e-006 7.0e-005 1.00e+000 9.564759203e+006 -7.936085644e+003 5.3e-016 0.84
28 2.7e-014 2.8e-006 7.0e-005 1.00e+000 9.555868567e+006 -7.936082902e+003 5.3e-016 0.88
29 2.7e-014 2.7e-006 6.9e-005 1.00e+000 9.271646090e+006 -7.935995067e+003 5.1e-016 0.91
30 2.7e-014 2.7e-006 6.9e-005 1.00e+000 9.263041679e+006 -7.935992235e+003 5.1e-016 0.94
31 2.7e-014 2.7e-006 6.9e-005 1.00e+000 9.245849659e+006 -7.935986565e+003 5.1e-016 0.97
32 2.5e-014 2.7e-006 6.9e-005 1.00e+000 9.177215869e+006 -7.935963845e+003 5.1e-016 1.01
33 2.6e-014 2.7e-006 6.9e-005 1.00e+000 9.143167056e+006 -7.935952396e+003 5.1e-016 1.08
34 2.6e-014 2.6e-006 6.8e-005 1.00e+000 9.109251218e+006 -7.935940904e+003 5.0e-016 1.13
35 2.7e-014 2.6e-006 6.8e-005 1.00e+000 9.108723228e+006 -7.935940724e+003 5.0e-016 1.17
36 2.7e-014 2.6e-006 6.8e-005 1.00e+000 9.106611619e+006 -7.935940004e+003 5.0e-016 1.22
37 2.7e-014 2.6e-006 6.8e-005 1.00e+000 9.039065649e+006 -7.935916925e+003 5.0e-016 1.26
38 2.7e-014 2.6e-006 6.8e-005 1.00e+000 9.036971068e+006 -7.935916199e+003 5.0e-016 1.33
39 2.7e-014 2.6e-006 6.8e-005 1.00e+000 9.032783729e+006 -7.935914744e+003 5.0e-016 1.39
40 2.7e-014 2.6e-006 6.8e-005 1.00e+000 9.032260419e+006 -7.935914563e+003 5.0e-016 1.42
41 2.7e-014 2.6e-006 6.8e-005 1.00e+000 9.030166919e+006 -7.935913838e+003 5.0e-016 1.47
42 2.7e-014 2.6e-006 6.8e-005 1.00e+000 9.029120492e+006 -7.935913477e+003 5.0e-016 1.53
43 2.7e-014 2.6e-006 6.8e-005 1.00e+000 9.028073988e+006 -7.935913116e+003 5.0e-016 1.59
44 2.7e-014 2.6e-006 6.8e-005 1.00e+000 9.025981804e+006 -7.935912392e+003 5.0e-016 1.64
45 2.7e-014 2.6e-006 6.8e-005 1.00e+000 9.024935832e+006 -7.935912030e+003 5.0e-016 1.67
46 2.7e-014 2.6e-006 6.8e-005 1.00e+000 9.024935832e+006 -7.935912030e+003 5.0e-016 1.70
Interior-point optimizer terminated. Time: 1.73.

Optimizer terminated. Time: 1.78

Interior-point solution summary
Problem status : UNKNOWN
Solution status : UNKNOWN
Primal. obj: 9.0249358317e+006 nrm: 1e+008 Viol. con: 2e+003 var: 0e+000 cones: 5e-007
Dual. obj: -7.9359120301e+003 nrm: 3e+011 Viol. con: 0e+000 var: 6e+003 cones: 0e+000
Optimizer summary
Optimizer - time: 1.78
Interior-point - iterations : 47 time: 1.73
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
this is the result sloved with mosek+cvxquad,but it is still failed

2

It may be that the Mosek solution is optimal. Is the solution primal feasible (or close enough) and usable for your purposes? I think CVX reported the status as Failed because Mosek reported UNKNOWN status(es). I don;t know whether CVX properly transforms (tries to) the Mosek results back to your original problem in such a case; and have to defer to the CVX developer @mcg fo answer that.

PRSTATUS converged to 1.00 which I think is good (or at least not bad), but perhaps residuals aren’t small enough to meet optimality criteria.

Anyhow, I defer to Mosek personnel to give a better assessment if they can do so based on the solver output. You may need to be patient as they may not visit the forum on the weekend.

3

Thanks for your reply,Mark_L_Stone!
with sdpt3 ,I get the results of the optimized variables, and they are almost all reasonable, but the optimization state fails, with mosek+cvxquad, it’s failed, the optimization result is not obtained, so does sedumi , it is so weird, I don’t know how to solve it.

4

Well, you can always retrieve the solution from Mosek (I don’t know if cvx allows it and how) and evaluate yourself if it is good enough for your purposes. The duality gap looks very bad, the violations are large, and the solution has huge norm, so something is numerically nasty about the problem. You are welcome to send a task file to Mosek support email.

5

I would not trust the solution given

I am fairly sure the problem is very bad. My guess is it is ill posed.
It might be an artifact of the problem is solved the successive approximation method.

6

@Erling That Mosek output is not from the successive approximation method, it is from Mosek being called to solve the problem produced by CVXQUAD conversions. I believe CVXQUAD produced 2 by 2 LMIs, which CVX converts to Second Order Cones before passing to Mosek. But we haven’t seen the original problem, complete with input data.

The output at the very beginning of the post shows the successive approximation method with SDPT3, but that output does not include solver output from each successive approximation iteration. By contrast, when CVXQUAD is used, a single problem is formulated and sent to Mosek, and that output from Mosek is what is shown.

7

Sorry, it confused me.

But my conclusion stands that the solution produced by Mosek most likely is no good and the problem is likely to be ill posed.

I have to have my hands on the problem to say something more conclusively.

8

It would be interesting to see how Mosek 9 would handle it using native exponential cone capability.

Unfortunately, there is not currently a version of CVX which can exploit Mosek 9’s native exponential cone capability, and I’m not sure whether or when there ever will be. CVX 3.0beta can exploit the native exponential cone capability of SCS and ECOS, although CVX 3.0beta has numerous bugs.

9

It works very well on all the test problems we have and we have quite some. I am fairly sure it will beat any of the approximation methods. Whether it will enter Cvx I do not know.

@mcg can remove the special GP mode in that case and just rely on the exponential cone so that would be a simplification I suppose. IMO just use

https://docs.mosek.com/modeling-cookbook/expo.html#geometric-programming

for GPs.