Disjunctive programming and relaxations of polyhedra

Conforti, Michele ; Del Pia, Alberto

In: Mathematical Programming, 2014, vol. 144, no. 1-2, p. 307-314

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    Summary
    Given a polyhedron $$L$$ with $$h$$ facets, whose interior contains no integral points, and a polyhedron $$P$$ , recent work in integer programming has focused on characterizing the convex hull of $$P$$ minus the interior of $$L$$ . We show that to obtain such a characterization it suffices to consider all relaxations of $$P$$ defined by at most $$n(h-1)$$ among the inequalities defining $$P$$ . This extends a result by Andersen, Cornuéjols, and Li.