Giacomo Zambelli

Maximal lattice-free convex sets in linear subspaces

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 Lovasz characterizing maximal lattice-free convex sets in Rn.

A Geometric Perspective on Lifting

Recently it has been shown that minimal inequalities for a continuous relaxation of mixed-integer linear programs are associated with maximal lattice-free convex sets. In this paper, we show how to lift these inequalities for integral nonbasic variables by considering maximal lattice-free convex sets in a higher dimensional space. We apply this approach to several examples. In particular, we identify cases in which the lifting is unique.

Minimal Inequalities for an Infinite Relaxation of Integer Programs

We show that maximal

Polyhedral approaches to mixed integer linear programming

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On degenerate multi-row Gomory cuts

-free convex sets are polyhedra when

Extended formulations in combinatorial optimization

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A counterexample to a conjecture of Gomory and Johnson

is the set of integral points in some rational polyhedron of

Equivalence between intersection cuts and the corner polyhedron

\mathbb{R}^n

On lifting integer variables in minimal inequalities

. 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

Odd Hole Recognition in Graphs of Bounded Clique Size

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