Four decades ago, Gomory introduced the corner polyhedron as a relaxation of a mixed
integer set in tableau form and Balas introduced intersection cuts for the corner polyhedron …

It is undeniable that geometric ideas have been very important to the foundations of modern
discrete optimization. The influence that geometric algorithms have in optimization was …

While many classes of cutting-planes are at the disposal of integer programming solvers, our
scientific understanding is far from complete with regards to cutting-plane selection, ie, the …

In Chaps. 5 and 6 we have introduced several classes of valid inequalities that can be used
to strengthen integer programming formulations in a cutting plane scheme. All these valid …

We consider the separation problem for sets X that are pre-images of a given set S by a
linear mapping. Classical examples occur in integer programming, as well as in other …

We show that maximal S-free convex sets are polyhedra when S is the set of integral points
in some rational polyhedron of R^n. This result extends a theorem of Lovász characterizing …

This paper introduces cutting planes that involve minimal structural assumptions, enabling
the generation of strong polyhedral relaxations for a broad class of problems. We consider …

Motivated by recent advances in solution methods for mixed-integer convex optimization
(MICP), we study the fundamental and open question of which sets can be represented …

Recently minimal and extreme inequalities for continuous group relaxations of general
mixed integer sets have been characterized. In this paper, we consider a stronger relaxation …

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 …