2003•Optimization methods & softwareRequires access

Second Order Cone Programming Relaxation of a Positive Semidefinite Constraint

Sun Young Kim, Masakazu Kojima, Makoto Yamashita

Abstract

The positive semidefinite constraint for the variable matrix in semidefinite programming (SDP) relaxation is further relaxed by a finite number of second order cone constraints in second order cone programming (SOCP) relaxations. A few types of SOCP relaxations are obtained from different ways of expressing the positive semidefinite constraint of the SDP relaxation. We present how such SOCP relaxations can be derived, and show the relationship between the resulting SOCP relaxations.

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Key concepts: Semidefinite programming, Second-order cone programming, Relaxation (psychology), Positive-definite matrix, Cone (formal languages), Quadratically constrained quadratic program, Mathematics, Semidefinite embedding