On some generalizations of the split closure

Sanjeeb Dash, Oktay Günlük, Diego Alejandro Morán Ramirez

Abstract

Split cuts form a well-known class of valid inequalities for mixed-integer programming problems (MIP). Cook et al. (1990) showed that the split closure of a rational polyhedron P is again a polyhedron. In this paper, we extend this result from a single rational polyhedron to the union of a finite number of rational polyhedra. We also show how this result can be used to prove that some generalizations of split cuts, namely cross cuts, also yield closures that are rational polyhedra.

Original languageEnglish
Title of host publicationInteger Programming and Combinatorial Optimization - 16th International Conference, IPCO 2013, Proceedings
Pages145-156
Number of pages12
DOIs
StatePublished - 2013
Externally publishedYes
Event16th Conference on Integer Programming and Combinatorial Optimization, IPCO 2013 - Valparaiso, Chile
Duration: 18 Mar 201320 Mar 2013

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume7801 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference16th Conference on Integer Programming and Combinatorial Optimization, IPCO 2013
Country/TerritoryChile
CityValparaiso
Period18/03/1320/03/13

Keywords

  • Cross cuts
  • closure
  • polyhedrality

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