The SCIP Optimization Suite provides a collection of software packages for mathematical
optimization centered around the constraint integer programming framework SCIP. This …

For over 10 years, the constraint integer programming framework SCIP has been extended
by capabilities for the solution of convex and nonconvex mixed-integer nonlinear programs …

Quadratically constrained quadratic programs (QCQPs) are optimization models whose
remarkable expressiveness have made them a cornerstone of methodological research for …

Using the recently proposed maximal quadratic-free sets and the well-known monoidal
strengthening procedure, we show how to improve intersection cuts for quadratically …

The generation of strong linear inequalities for QCQPs has been recently tackled by a
number of authors using the intersection cut paradigm—a highly studied tool in integer …

The intersection cut framework was introduced by Balas in 1971 as a method for generating
cutting planes in integer optimization. In this framework, one uses a full-dimensional convex …

We study a mixed-integer set S:={(x, t)∈{0, 1} n× R: f (x)≥ t} arising in the submodular
maximization problem, where f is a submodular function defined over {0, 1} n. We use …

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 …

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 …

Cutting planes are of crucial importance when solving nonconvex nonlinear programs to
global optimality, for example using the spatial branch-and-bound algorithms. In this paper …