Generating cutting planes for the semidefinite relaxation of quadratic programs

Abstract

Semidefinite Programming is well-known for providing relaxations of quadratic programs. In practice, only few real-world applications of this approach have been reported. This can be explained by the fact that the standard semidefinite relaxation must generally be tightened with cuts, which increases the substantial computational cost of the semidefinite program. Then, the challenge is to come up with the most effective cuts.In this paper, we present a systematic approach based on a polynomial separation problem to compute such cuts. Then, we apply this technique to a well-known problem of energy management, i.e., the scheduling of the nuclear outages which is a combinatorial problem with quadratic objective and non-convex quadratic constraints. This leads to the identification of some relevant cutting planes for this problem, allowing an average enhancement of 25% of the semidefinite relaxation compared to the linear relaxation.