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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?

user436994
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1 Answers1

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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.

Erwin Kalvelagen
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  • But Cplex is in general able to handle quadratic constraints. Do you mean that Cplex cannot deal with quadratic constraints in this special case as the objective function is non-convex? – user436994 Apr 27 '17 at 20:02
  • No, you are mistaken in your first statement. Cplex cannot handle general quadratic constraints. It can only handle convex quadratic constraints (with either a linear or convex quadratic objective). Again, Cplex only supports a non-convex quadratic objective if the constraints are linear. Please consult the Cplex documentation for further information. – Erwin Kalvelagen Apr 27 '17 at 20:38