Maximal lattice-free convex sets in linear subspaces

Abstract

We consider a model that arises in integer programming, and show that all irredundant inequalities are obtained from maximal lattice-free convex sets in an affine subspace. We also show that these sets are polyhedra. The latter result extends a theorem of Lovász characterizing maximal lattice-free convex sets in ${\mathbb{R}}^n$.

Cited by in corpus (10)

• Light on the Infinite Group Relaxation
• Unique lifting of integer variables in minimal inequalities
• A geometric approach to cut-generating functions
• Equivariant Perturbation in Gomory and Johnson's Infinite Group Problem. I. The One-Dimensional Case
• Unique Minimal Liftings for Simplicial Polytopes
• Equivariant Perturbation in Gomory and Johnson's Infinite Group Problem. III. Foundations for the k-Dimensional Case with Applications to k=2
• On Subadditive Duality for Conic Mixed-Integer Programs
• A study of rank-one sets with linear side constraints and application to the pooling problem
• A local maximizer for lattice width of $3$-dimensional hollow bodies
• Mixed-integer convex representability