Binary quadratic optimization problems that are difficult to solve by conic relaxations
- 주제(키워드) A hierarchy of semidefinite relaxations , Binary integer quadratic program , Conic relaxations , Inexact optimal values , The max-cut problem with equal weight
- 관리정보기술 faculty
- 등재 SCIE, SCOPUS
- 발행기관 Elsevier B.V.
- 발행년도 2017
- 총서유형 Journal
- URI http://www.dcollection.net/handler/ewha/000000139448
- 본문언어 영어
- Published As http://dx.doi.org/10.1016/j.disopt.2016.08.001
초록/요약
We study conic relaxations including semidefinite programming (SDP) relaxations and doubly nonnegative programming (DNN) relaxations to find the optimal values of binary QOPs. The main focus of the study is on how the relaxations perform with respect to the rank of the coefficient matrix in the objective of a binary QOP. More precisely, for a class of binary QOP instances, which include the max-cut problem of a graph with an odd number of nodes and equal weight, we show numerically that (1) neither the standard DNN relaxation nor the DNN relaxation derived from the completely positive formulation by Burer performs better than the standard SDP relaxation, and (2) Lasserre's hierarchy of SDP relaxations requires solving the SDP with the relaxation order at least . ⌈n/2⌉ to attain the optimal value. The bound . ⌈n/2⌉ for the max-cut problem of a graph with equal weight is consistent with Laurent's conjecture in 2003, which was proved recently by Fawzi, Saunderson and Parrilo in 2015. © 2016 Elsevier B.V.
more