The Moment-SOS Hierarchy
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.
Praktische info:
Leertraject
georganiseerd door:
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.
Lesgever/spreker
Onderzoeker bij LAAS-CNRS, Toulouse, Frankrijk
Professor aan de Tsjechische Technische Universiteit in Praag, Tsjechië
Back to the Roots Seminar Series
The ERC research project "Back to the roots of data-driven dynamical system identification", led by Prof. Dr. Bart De Moor (KU Leuven, ESAT-STADIUS), focuses on system identification, where mathematical models are derived from observed data generated by systems such as medical monitoring, electricity consumption and industrial processes. Utilizing optimization algorithms, one seeks to identify the best model in a chosen model class. This methodology finds widespread application across thousands of use cases within the AI community. However, there is no guarantee that optimization algorithms will find the best model. Present-day optimization practices are heuristic in nature, yielding results that may not be reproducible and consequently difficult to interpret.
The main objective of the Back to the Roots project is to develop a theoretical framework that combines model classes and optimization algorithms, enabling the calculation of the optimal model within the specified model class with 100% certainty.
