Unique Minimal Liftings for Simplicial Polytopes

Abstract

For a minimal inequality derived from a maximal lattice-free simplicial polytope in ${\mathbb{R}}^n$, we investigate the region where minimal liftings are uniquely defined, and we characterize when this region covers ${\mathbb{R}}^n$. We then use this characterization to show that a minimal inequality derived from a maximal lattice-free simplex in ${\mathbb{R}}^n$ with exactly one lattice point in the relative interior of each facet has a unique minimal lifting if and only if all the vertices of the simplex are lattice points.

15 pages

References in corpus (2)

• Maximal lattice-free convex sets in linear subspaces
• Intersection Cuts with Infinite Split Rank

Cited by in corpus (2)

• Light on the Infinite Group Relaxation
• A geometric approach to cut-generating functions