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The Equivalence Between Doubly Nonnegative Relaxation and Semidefinite Relaxation for Binary Quadratic Programming Problems by Guo, Chuan-Hao; Bai, Yan-Qin; Tang, Li-Ping is a scholarly article available to read on EtoBox.

What is The Equivalence Between Doubly Nonnegative Relaxation and Semidefinite Relaxation for Binary Quadratic Programming Problems about?

It has recently been shown (Burer, Math. Program Ser. A 120:479-495, 2009) that a large class of NP-hard nonconvex quadratic programming problems can be modeled as so called completely positive programming problems, which are convex but still NP-hard in general. A basic tractable relaxation is gotten by doubly nonnegative relaxation, resulting in a doubly nonnegative programming. In this paper, we prove that doubly nonnegative relaxation for binary quadratic programming (BQP) problem is equivalent to a tighter semidifinite relaxation for it. When problem (BQP) reduces to max-cut (MC) problem, doubly nonnegative relaxation for it is equivalent to the standard semidifinite relaxation. Furthermore, some compared numerical results are reported.

Author

Guo, Chuan-Hao; Bai, Yan-Qin; Tang, Li-Ping

Published

2012

Language

EN