Location: Paris-Dauphine, room A707 / Time: 10h30-12h30
Jean Louët (U. Paris-Dauphine)
Titre: Gradient approximation of the Monge problem
Résumé: We investigate the approximation of the L^1-optimal transport problem with a vanishing Dirichlet energy \eps\int|DT|^2. We study the \Gamma-convergence as \eps goes to 0, by showing a density result, among the set of transport maps between two fixed measures, or such maps which are also Sobolev (and even Lipschitz). We analyze in detail a class of examples where no Sobolev optimal transport map exists, and study both the selected maps at the limit, which possibly differ from the monotone transport map, and the asymptotics of the optimal cost depending on \eps, where the limit term has order \eps|\log\eps|. This is a joint work with L. De Pascale (Pisa) and F. Santambrogio (Paris-Sud).”
Aude Genevay (Mokaplan Inria/U. Paris-Dauphine)
Titre: Sochastic Optimization for Optimal Transport
