Minimal Valid Inequalities for Integer Constraints

Authors:
Valentin Borozan;Gérard Cornuéjols
Affiliations:
LIF, Faculté des Sciences de Luminy, Université de Marseille, 13288 Marseille, France;Tepper School of Business, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, and LIF, Faculté des Sciences de Luminy, Université de Marseille, 13288 Marseille, France
Venue:
Mathematics of Operations Research
Year:
2009

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Abstract

In this paper, we consider a semi-infinite relaxation of mixed-integer linear programs. We show that minimal valid inequalities for this relaxation correspond to maximal lattice-free convex sets, and that they arise from nonnegative, piecewise linear, positively homogeneous, convex functions.