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 this paper, we present an analysis of the strength of sparse cutting planes for mixed
integer linear programs (MILP) with sparse formulations. We examine three kinds of …

The Stabbing Planes proof system was introduced to model the reasoning carried out in
practical mixed integer programming solvers. As a proof system, it is powerful enough to …

A bipartite bilinear program (BBP) is a quadratically constrained quadratic optimization
problem where the variables can be partitioned into two sets such that fixing the variables in …

Many operations related optimization problems involve repeatedly solving similar mixed
integer linear programming (MILP) instances with the same constraint matrix but differing …

We propose a method to generate cutting-planes from multiple covers of knapsack
constraints. The covers may come from different knapsack inequalities if the weights in the …

A classical approach for obtaining valid inequalities for a set involves the analysis of
relaxations constructed using aggregations of the inequalities that describe such a set …

We study properties of the convex hull of a set described by quadratic inequalities. A simple
way of generating inequalities valid on is to take nonnegative linear combinations of the …

The goal of this paper is to derive new classes of valid convex inequalities for quadratically
constrained quadratic programs (QCQPs) through the technique of lifting. Our first main …

In this paper, we study the strength of convex relaxations obtained by convexification of
aggregation of constraints for a set $ S $ described by two bilinear bipartite equalities …