Unique Minimal Liftings for Simplicial Polytopes

Authors:
Amitabh Basu;Gérard Cornuéjols;Matthias Köppe
Affiliations:
Department of Mathematics, University of California, Davis, Davis, California 95616;Tepper School of Business, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213;Department of Mathematics, University of California, Davis, Davis, California 95616
Venue:
Mathematics of Operations Research
Year:
2012

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Abstract

For a minimal inequality derived from a maximal lattice-free simplicial polytope in Rn, we investigate the region where minimal liftings are uniquely defined, and we characterize when this region covers Rn. We then use this characterization to show that a minimal inequality derived from a maximal lattice-free simplex in Rn 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.