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

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## 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: | 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: | Polyhedral combinatorics ; Semidefinite programming ; Max-cut problem ; Clique partitioning problem ; Quadratic 0–1 programming |

Subjects: | |

Departments: | Lancaster University Management School > Management Science |

ID Code: | 50252 |

Deposited By: | ep_importer_pure |

Deposited On: | 04 Oct 2011 16:12 |

Refereed?: | Yes |

Published?: | Published |

Last Modified: | 22 Oct 2016 02:17 |

Identification Number: | |

URI: | http://eprints.lancs.ac.uk/id/eprint/50252 |
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