Minimal Inequalities for an Infinite Relaxation of Integer Programs
Amitabh Basu, Michele Conforti, Gérard Cornuéjols, Giacomo Zambelli · SIAM Journal on Discrete Mathematics · 2010
We show that maximal S-free convex sets are polyhedra when S is the set of integral points in some rational polyhedron of $\mathbb{R}^n$. This result extends a theorem of Lovász characterizing maximal lattice-free convex sets. Our theorem has implications in integer programming. In particular, we show that maximal S-free convex sets are in one-to-one correspondence with minimal inequalities.