Theory of linear and integer programming
Theory of linear and integer programming
Inequalities from Two Rows of a Simplex Tableau
IPCO '07 Proceedings of the 12th international conference on Integer Programming and Combinatorial Optimization
Minimal Valid Inequalities for Integer Constraints
Mathematics of Operations Research
On degenerate multi-row Gomory cuts
Operations Research Letters
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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.