An issue of solving quadratic programming

[wang lingyi]

Hi,

I am trying to solve a quadratic programming (QP) problem using mosek within matlab 2018a. My problem has equality and inequality constraints. The mathematical description of optimization problem is attached as below. I respectively use quadprog function from matlab and mosek to solve the QP. I find that mosek always report exiflag=  -1 in the first iteration while matlab quadprog function can work and find the minimum. I guess it results from the equality constraint that makes the mosek hard to cope with. How can I deal with this problem? 

Thank you very much for any useful advice~

[Michal Adamaszek]

Impossible to say anything useful without a reproducible example or at least a complete log output.

Having an equality constraint is itself not an issue.

Here is the documentation in case you want to increase verbosity and/or save a task file https://docs.mosek.com/latest/toolbox/reference.html#quadprog

Michal

[Erling D. Andersen]

Could be H is not positive semi-definite or otherwise ill-conditioned.

Maybe quadprog accepts such problems.

[Mark L. Stone]

MATLAB's quadprog accepts all QPs, convex or non-convex.

[Mark L. Stone]

MATLAB's quadprog attempts to find local (not global) minimum of non-convex QPs.

[wang lingyi]

Thank you for your advice. Attached below is my Diagnostics output. I surprisingly find that it shows that primal and dual feasible, while the exitflag= -1. And I tried to write my prob structure to an output file, but what format should I output ? In the instruction link listed above, it is myprob.opf. Is that ok that my output file is in opf format? Attached below is my programming interface. 

      

 

[Michal Adamaszek]

You may be right, I suspect that the stall termination code is not handled properly and leads to the -1. It's a minor bug we will need to fix.

In the meantime if all you want to do is solve QPs then find the file mskeflag.m in your toolbox installation and change line 6 from

if rcode==0 && isfield(res,'sol')

to

if isfield(res,'sol')

and see if that gives exitflag=1

[wang lingyi]

yeah, it gives exactly exitflag=1

[Michal Adamaszek]

Thanks for confirming. So just to clarify, the bug is only in a bit careless converting the response code from the solver into an exitflag, and not in the actual solution. Since this is a bit obscure corner of the API and the fix should work for you, it is possible we will just fix it officially in the upcoming version 10 and leave 9.3 as it is.

Thanks for reporting.