The equivalence between doubly nonnegative relaxation and semidefinite relaxation for binary quadratic programming problems
Abstract
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.
Cite
@article{arxiv.1211.5406,
title = {The equivalence between doubly nonnegative relaxation and semidefinite relaxation for binary quadratic programming problems},
author = {Chuan-Hao Guo and Yan-Qin Bai and Li-Ping Tang},
journal= {arXiv preprint arXiv:1211.5406},
year = {2012}
}