In 1971, Balas introduced the intersection cut framework as a method for generating separating hyperplanes (or “cuts”) in integer optimization. These cuts are derived from convex S-free sets, and inclusion-wise maximal S-free sets yield the strongest intersection cuts. When S is a lattice, maximal S-free sets are well-studied from theoretical and computational standpoints. In this talk, we focus on the case when S is defined by a non-convex quadratic inequality and show how to construct basic maximal quadratic-free sets. Additionally, we explore how to generalize the basic procedure to construct a plethora of new maximal quadratic-free sets for homogeneous quadratics. Joint work with Antonia Chmiela, Joseph Paat, and Felipe Serrano.
Date of closure: Aug 23, 2023
Venue: Sala de Seminario John Von Neumann, CMM, Beauchef 851, Torre Norte, Piso 7.
Speaker: Gonzalo Muñoz
Affiliation: Universidad de O'Higgins
Coordinator: José Verschae