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 …

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 …

In this paper, we consider a semi-infinite relaxation of mixed-integer linear programs. We
show that minimal valid inequalities for this relaxation correspond to maximal lattice-free …

A convex set with nonempty interior is maximal lattice-free if it is inclusion maximal with
respect to the property of not containing integer points in its interior. Maximal lattice-free …

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 …

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 …

The cutting-plane approach to integer programming was initiated more than 40 years ago:
Gomory introduced the corner polyhedron as a relaxation of a mixed integer set in tableau …

In this chapter, we provide an overview of the mathematical foundations and recent
theoretical and computational advances in the study of the grouptheoretic approach in …

In this paper, we study the relationship between 2D lattice-free cuts, the family of cuts
obtained by taking two-row relaxations of a mixed-integer program (MIP) and applying …

A simple relaxation consisting of two rows of a simplex tableau is a mixed-integer set with
two equations, two free integer variables, and nonnegative continuous variables. Recently …