I have a QP with a quadratic constraint. The objective is nonPSD 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 nonPSD 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.
Topic

Re: Solution Target = 2 with non PSD objective but with PSD constraint
20130104T17:35:34ZThis is the accepted answer. This is the accepted answer.I'm afraid CPLEX will not be able to solve your problem.
CPLEX can find a local solution to nonconvex QP, i.e. nonconvex quadratic objective subject to linear constraints. To do this you set the solution target to 2.
However, your problem is a nonconvex QCP, i.e. nonconvex quadratic objective subject to quadratic constraints. This is something CPLEX cannot solve, even if your quadratic constraints are convex.
Christian. 
Re: Solution Target = 2 with non PSD objective but with PSD constraint
20130105T07:04:04ZThis is the accepted answer. This is the accepted answer. Christian Bliek
 20130104T17:35:34Z
I'm afraid CPLEX will not be able to solve your problem.
CPLEX can find a local solution to nonconvex QP, i.e. nonconvex quadratic objective subject to linear constraints. To do this you set the solution target to 2.
However, your problem is a nonconvex QCP, i.e. nonconvex quadratic objective subject to quadratic constraints. This is something CPLEX cannot solve, even if your quadratic constraints are convex.
Christian.
Just wanted to say that the solution target feature is very helpful for solving nonconvex QPs which we encounter in less than 1% of cases.
Regards,
Vivek.