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On the polyhedrality of cross and quadrilateral closures

oktay gunluk (gunluk***at***us.ibm.com)
sanjeeb dash (sanjeebd***at***us.ibm.com)
diego moran (dmoran***at***gatech.edu)

Abstract: Split cuts form a well-known class of valid inequalities for mixed-integer programming problems. Cook, Kannan and Schrijver (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 then use this result to prove that cross cuts yield closures that are rational polyhedra. Cross cuts are a generalization of split cuts introduced by Dash, Dey and Gunluk (2012). Finally, we show that the quadrilateral closure of the two-row continuous group relaxation is a polyhedron, answering an open question in Basu, Bonami, Cornuejols and Margot (2011).

Keywords: Cutting planes, cross cuts, quadrilateral cuts

Category 1: Integer Programming ((Mixed) Integer Linear Programming )

Citation: IBM Research Report

Download: [PDF]

Entry Submitted: 12/09/2014
Entry Accepted: 12/09/2014
Entry Last Modified: 01/19/2016

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