Second order cone programming relaxation of nonconvex quadratic optimization problems

Abstract

A disadvantage of the SDP (semidefinite programming) relaxation method for quadratic and/or combinatorial optimization problems lies in its expensive computational cost. This paper proposes a SOCP (second-order-cone programming) relaxation method, which strengthens the lift-and-project LP (linear programming) relaxation method by adding convex quadratic valid inequalities for the positive semidefinite cone involved in the SDP relaxation. Numerical experiments show that our SOCP relaxation is a reasonable compromise between the effectiveness of the SDP relaxation and the low computational cost of the lift-and-project LP relaxation. © 2001 OPA (Overseas Publishers Association) N.V. Published by license under the Gordon and Breach Science Publishers imprint, a member of the Taylor & Francis Group.