On the polyhedrality of cross and quadrilateral closures

Sanjeeb Dash, Oktay Günlük, Diego A. Morán R

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6 Scopus citations


Split cuts form a well-known class of valid inequalities for mixed-integer programming problems. Cook et al. (Math Program 47:155–174, 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 et al. (Math Program 135:221–254, 2012). Finally, we show that the quadrilateral closure of the two-row continuous group relaxation is a polyhedron, answering an open question in Basu et al. (Math Program 126:281–314, 2011).

Original languageEnglish
Pages (from-to)245-270
Number of pages26
JournalMathematical Programming
Issue number1-2
StatePublished - 1 Nov 2016
Externally publishedYes


  • Closure
  • Cross cuts
  • Integer programming
  • Polyhedrality


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