ORIE Colloquium: Gonzalo Muñoz (Universidad de Chile)
Separating hyperplanes for non-convex quadratically-constrained optimization
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 a non-convex quadratic inequality defines S 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.
This is joint work with Antonia Chmiela, Joseph Paat, and Felipe Serrano.
Bio:
Gonzalo Muñoz is an assistant professor at the Industrial Engineering Department of Universidad de Chile and a researcher at the Institute of Complex Systems in Engineering, Chile. He obtained his Ph.D. from the Department of Industrial Engineering and Operations Research at Columbia University. His main interests include theoretical and computational developments in mixed integer linear and non-linear optimization. His work has received recognition from the optimization community, such as the 2023 INFORMS Optimization Society Young Researcher Prize.