A Geometric Perspective on Lifting

Authors:
Michele Conforti;Gérard Cornuéjols;Giacomo Zambelli
Affiliations:
Dipartimento di Matematica Pura ed Applicata, Università di Padova, 35121 Padova, Italy;Tepper School of Business, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213;London School of Economics and Political Sciences, London WC2A 2AE, United Kingdom
Venue:
Operations Research
Year:
2011

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Abstract

Recently it has been shown that minimal inequalities for a continuous relaxation of mixed-integer linear programs are associated with maximal lattice-free convex sets. In this paper, we show how to lift these inequalities for integral nonbasic variables by considering maximal lattice-free convex sets in a higher dimensional space. We apply this approach to several examples. In particular, we identify cases in which the lifting is unique.