Gurobi or CPLEX? Quadratic indefinite objective - quadratic positive-semidefinite constraints

Question

I want to minimize a quadratic objective function subject to a set of linear and quadratic constraints.

The quadratic objective function is indefinite (non-convex). The quadratic constraints are positive-semidefinite (convex). The variables are continuous.

Can I handle this with Gurobi or CPLEX? Which one is the better choice?

Answer 1

Gurobi handles convex problems only. Cplex can handle convex problems and certain classes of non-convex problems.

Cplex has an OptimalityTarget parameter to select the non-convex solver. Unfortunately it only supports QP and MIQP problems (i.e. only linear constraints).

Other global solvers you can try are Baron, GloMIQO, or Couenne.