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arXiv · 1701.06540

Minimal inequalities for an infinite relaxation of integer programs

Amitabh Basu·Michele Conforti·Gerard Cornuejols·Giacomo Zambelli
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Abstract

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 Lov\'asz 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.

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Amitabh Basu, Michele Conforti, Gerard Cornuejols, Giacomo Zambelli. 2017-01-23. Minimal inequalities for an infinite relaxation of integer programs. https://doi.org/10.1137/090756375

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