A Geometric Perspective on Lifting

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 where the lifting is sequence-independent, and therefore unique.