On the polyhedrality of cross and quadrilateral closures

نویسندگان

  • Sanjeeb Dash
  • Oktay Günlük
  • Diego A. Morán R.
چکیده

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 Günlük (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, Cornuéjols and Margot (2011).

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عنوان ژورنال:
  • Math. Program.

دوره 160  شماره 

صفحات  -

تاریخ انتشار 2016