Stationary point for nonconvex QCQP?
AnsweredDear Gurobi team,
I am working on a heuristic to solve a large nonconvex MIQCQP (1) that arises after discretizing a PDEconstrained optimal control problem. Fortunately, the problem can be transformed into a convex MIQCQP (2) by linearizing nonconvex quadratic constraints, i.e. the relaxed problem is convex.
In my heuristic, I'd like to solve the relaxation of (1), i.e. a nonconvex QCQP (3). Setting the Parameter NonConvex=2, Gurobi uses a spatial B&B algorithm to solve the problem to global optimality. Since I only need a stationary point, my idea was to terminate the spatial B&B with the first found feasible solution. Now I was wondering whether it is possible to solve (3) directly via the barrier method for a stationary point?
Thanks for your time.
Best,
Jonathan

Hi Jonathan,
It is currently not possible to use the Barrier algorithm in order to solve a nonconvex QCQP to get a local minimum. Please also note that the feasible solution point found by the spatial B&B algorithm is currently not guaranteed to be a stationary point.
You could get the solution of the convex relaxation of a nonconvex QCQP by solving the root relaxation and then getting the relaxation solution point from a \(\texttt{MIPNODE}\) callback.
Best regards,
Jaromił0
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