Speaker: Quentin Marigot (University of Orsay)
Abstract: Optimal transport has emerged as a suitable tool in various numerical applications, particularly in statistics, inverse problems, and PDE discretization. In the first half of this mini-course, I will present numerical methods to numerically solve optimal transport problems, focusing on methods base on Kantorovich duality. I will concentrate on entropy-regularized optimal transport and on semi-discrete optimal transport. The presentation will emphasize algorithmic considerations. The second half of the presentation will delve into recent advancements regarding the stability of optimal transport solutions. The question of (quantitative) stability has been largely overlooked, despite its necessity to justify most of the numerical and statistical methods relying on optimal transport. I will show how some classical functional inequalities can shed light on this question.
Biography: Quentin Mérigot is professor in Laboratoire de mathématiques d'Orsay at Université Paris-Saclay, with a secondment from the Institut universitaire de France. His research interests include optimal transport, inverse problems, numerical analysis and geometric methods for data analysis. The numerical methods he proposes often rely on techniques from optimization and computational geometry.