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# Minimal Inequalities for an Infinite Relaxation of Integer Programs

@article{Basu2010MinimalIF, title={Minimal Inequalities for an Infinite Relaxation of Integer Programs}, author={Amitabh Basu and Michele Conforti and G{\'e}rard Cornu{\'e}jols and Giacomo Zambelli}, journal={SIAM J. Discrete Math.}, year={2010}, volume={24}, pages={158-168} }

- Published 2010 in SIAM J. Discrete Math.
DOI:10.1137/090756375

We show that maximal S-free convex sets are polyhedra when S is the set of integral points in some rational polyhedron of R. 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 correspondance with minimal inequalities.