Monday, September 25
Invited Lecture: Semi-discrete approach to optimal transport and Monge-Ampère equations
Time: 17:30 - 18:30
Room: L1, Building L
Chair: Jean-Baptiste Caillau, Univ. Côte d’Azur & CNRS/Inria
Many problems in geometric optics or convex geometry can be recast as optimal transport problems: this includes the far-field reflector problem, Alexandrov's curvature prescription problem, etc. A popular way to solve these problems numerically is to assume that the source probability measure is absolutely continuous while the target measure is finitely supported. We refer to this setting as semi-discrete. In this talk, I will present a damped Newton's algorithm for semi-discrete optimal transport, applications of this algorithm to geometric optics, and its adaptation to Monge-Ampère equations with a non-linear right-hand side.