We show that maximal S-free convex sets are polyhedra when S is the set of integral points in some rational polyhedron of R(n). This result extends a theorem of Lovasz 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.
Minimal Inequalities For An Infinite Relaxation of Integer Programs
CONFORTI, MICHELANGELO;
2010
Abstract
We show that maximal S-free convex sets are polyhedra when S is the set of integral points in some rational polyhedron of R(n). This result extends a theorem of Lovasz 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.File in questo prodotto:
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