Topic
• 2 replies
• Latest Post - ‏2013-01-05T07:04:04Z by SystemAdmin
7929 Posts

# Pinned topic Solution Target = 2 with non PSD objective but with PSD constraint

‏2012-12-22T06:25:47Z |
I have a QP with a quadratic constraint. The objective is non-PSD but the constraint is PSD.

But I am unable to solve the problem to the first order optimality with solution target set to 2. The optimizer still complains about non-PSD of the objective. I guess solution target = 2 only applies to QPs. Would that be correct? If not, is there a way to solve the above problem to first order optimality?

Thanks,
Vivek.
Updated on 2013-01-05T07:04:04Z at 2013-01-05T07:04:04Z by SystemAdmin
• Christian Bliek
11 Posts

#### Re: Solution Target = 2 with non PSD objective but with PSD constraint

‏2013-01-04T17:35:34Z
I'm afraid CPLEX will not be able to solve your problem.

CPLEX can find a local solution to non-convex QP, i.e. non-convex quadratic objective subject to linear constraints. To do this you set the solution target to 2.

However, your problem is a non-convex QCP, i.e. non-convex quadratic objective subject to quadratic constraints. This is something CPLEX cannot solve, even if your quadratic constraints are convex.

Christian.
7929 Posts

#### Re: Solution Target = 2 with non PSD objective but with PSD constraint

‏2013-01-05T07:04:04Z
I'm afraid CPLEX will not be able to solve your problem.

CPLEX can find a local solution to non-convex QP, i.e. non-convex quadratic objective subject to linear constraints. To do this you set the solution target to 2.

However, your problem is a non-convex QCP, i.e. non-convex quadratic objective subject to quadratic constraints. This is something CPLEX cannot solve, even if your quadratic constraints are convex.

Christian.
Thanks Christian!

Just wanted to say that the solution target feature is very helpful for solving non-convex QPs which we encounter in less than 1% of cases.

Regards,
Vivek.