Binary positive semidefinite matrices and associated integer polytopes

Letchford, A N and Sorensen, M M (2012) Binary positive semidefinite matrices and associated integer polytopes. Mathematical Programming, 131 (1-2). pp. 253-271. ISSN 0025-5610

[thumbnail of Binary positive semidefinite matrices and associated integer polytopes]
Preview
PDF (Binary positive semidefinite matrices and associated integer polytopes)
10.pdf - Submitted Version

Download (384kB)

Abstract

We consider the positive semidefinite (psd) matrices with binary entries, along with the corresponding integer polytopes.We begin by establishing some basic properties of these matrices and polytopes. Then, we show that several families of integer polytopes in the literature—the cut, boolean quadric, multicut and clique partitioning polytopes—are faces of binary psd polytopes. Finally,we present some implications of these polyhedral relationships. In particular, we answer an open question in the literature on the max-cut problem, by showing that the rounded psd inequalities define a polytope.

Item Type:
Journal Article
Journal or Publication Title:
Mathematical Programming
Additional Information:
This is the full journal version of a paper that appeared as a chapter in the 2008 IPCO volume.
Uncontrolled Keywords:
/dk/atira/pure/core/keywords/managementscience
Subjects:
?? polyhedral combinatoricssemidefinite programmingmax-cut problemclique partitioning problemquadratic 0–1 programmingmanagement sciencesoftwaremathematics(all)discipline-based research ??
ID Code:
50252
Deposited By:
Deposited On:
04 Oct 2011 15:12
Refereed?:
Yes
Published?:
Published
Last Modified:
27 Mar 2024 00:40