Both problem and solution status are unknown

[Jianqiao Huang]

Hi Mosek,

I call Mosek through Yalmip. The report of Mosek is as follows,

Interior-point solution summary
  Problem status  : UNKNOWN
  Solution status : UNKNOWN
  Primal.  obj: -2.3465823848e+00   nrm: 2e+03    Viol.  con: 4e+03    var: 0e+00    barvar: 0e+00    cones: 0e+00  
  Dual.    obj: -2.3160623778e+00   nrm: 6e+02    Viol.  con: 0e+00    var: 3e-02    barvar: 1e-04    cones: 0e+00  
Optimizer summary
  Optimizer                 -                        time: 7.84.    

How can I fix this problem?

Thanks,

Jianqiao Huang

[Erling D. Andersen]

I suggest you read

https://docs.mosek.com/latest/toolbox/debugging-log.html#solution-summary

It is impossible based on the information provide to say anything about why your optimization problem is hard.

We need at least the complete log output.

[Jianqiao Huang]

Hi Andersen,

I have attached the Mosek task file. Can you diagnose my problem?

Thanks,

Jianqiao Huang

[Jianqiao Huang]

Hi Mosek,

If you need more information about my model, please let me know.

Thanks,

Jianqiao Huang

[Erling D. Andersen]

I have had a look at your problem. I cannot pinpoint a bad thing about your problem.

Here is what happens.

In every iterations Mosek has to solve a linear equation system. In involves computing a Cholesky factorization

of a symmetric matrix which in theory is positive definite. However, in this case as often happens it becomes semi-definite only.

Next Mosek tries to deal with the singularity using its usual methods/tricks. However, in this case they do not work sufficiently well

and Mosek has to give up. This happens fortunately rarely but for the moment being we do not have a solution that makes your problem solvable.

Sorry.

[Jianqiao Huang]

Hello Erling D,

Thanks for your reply. Is the matrix you mentioned Schur complement matrix? What parameters should I tune/revise to make the matrix positive definite? Is it possible to know what equality or inequality constraints make the matrix singular?

Thanks,

Jianqiao Huang

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[Erling D. Andersen]

It is impossible to say anything meaningful about what you should change in your model. 

For instance for LP the matrix in question is

A*diag(x)*diag(s)^{-1}A^T

so it is dependent on the primal (=x) and dual (=s) solutions.

[Jianqiao Huang]

Hello  Andersen,

Is it something wrong with matrix A? Can you check whether A is full rank?

Thanks,

Jianqiao Huang

[Erling D. Andersen]

No. And I cannot easily check your matrix. In this case we cannot help you. Sorry.

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