Didier Henrion
Researcher at LAAS-CNRS, Toulouse, France
Professor at the Czech Technical University in Prague, Czechia
The Moment-SOS hierarchy
20 February 2024, 5pm
KU Leuven, Thermotechnisch Instituut
Aula van de Tweede Hoofdwet (01.02)
Abstract
Polynomial optimization consists of minimizing a polynomial of many real variables subject to polynomial equality and inequality constraints. Its special case is the problem of finding real solutions of a system of polynomial equations. This difficult problem has many applications in fields such as statistics, signal processing, machine learning, computer vision, computational geometry, and control engineering. The Moment-SOS hierarchy is an approach to polynomial optimization that solves it globally at the price of solving a family of convex (semidefinite) optimization problems of increasing size. The lecture introduces the approach and describes its main milestones during the last two decades. The focus is on the computational features of the Moment-SOS hierarchy, its limitations and current efforts to overcome them.