Semidefinite relaxations for mixed 0-1 second-order cone program

Authors:
Agnès Gorge;Abdel Lisser;Riadh Zorgati
Affiliations:
LRI, Université Paris-Sud Orsay, Orsay, France;LRI, Université Paris-Sud Orsay, Orsay, France;EDF R&D, OSIRIS, Clamart, France
Venue:
ISCO'12 Proceedings of the Second international conference on Combinatorial Optimization
Year:
2012

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Abstract

We investigate semidefinite relaxations for mixed 0-1 Second-Order Cone Programs. Central to our approach is the reformulation of the problem as a non convex Quadratically Constrained Quadratic Program (QCQP), an approach that situates this problem in the framework of binary quadratically constrained quadratic programming. This allows us to apply the well-known semidefinite relaxation for such problems. This relaxation is strengthened by the addition of constraints of the initial problem expressed in the form of semidefinite constraints. We report encouraging computational results indicating that the semidefinite relaxation improves significantly the continuous relaxation (112% on average) and that it often provides a lower bound very close to the optimal value. In addition, the computational time for obtaining these results remains reasonable.