Minimal Inequalities for an Infinite Relaxation of Integer Programs

We show that maximal S-free convex sets are polyhedra when S is the set of integral points in some rational polyhedron of Rⁿ. This result extends a theorem of Lovász characterizing maximal lattice-free convex sets. We then consider a model that arises in integer programming, and show that all irredundant inequalities are obtained from maximal S-free convex sets.