Paper Info
Title
Binary quadratic optimization problems that are difficult to solve by conic relaxations.
Abstract
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.
Year
DOI
Venue
2017
10.1016/j.disopt.2016.08.001
Discrete Optimization
Keywords
Field
DocType
Binary integer quadratic program,The max-cut problem with equal weight,Conic relaxations,A hierarchy of semidefinite relaxations,Inexact optimal values
Discrete mathematics,Graph,Mathematical optimization,Combinatorics,Coefficient matrix,Quadratic programming,Hierarchy,Conic section,Conjecture,Mathematics,Semidefinite programming,Binary number
Journal
Volume
ISSN
Citations 
24
1572-5286
1
PageRank 
References 
Authors
0.35
7
2
Name
Order
Citations
PageRank
S. Kim124814.25
Masakazu Kojima21603222.51