Nov 17 – 18, 2022
Université Claude Bernard Lyon I, campus de la Doua.
Europe/Paris timezone

Stability in optimal transport and strong c-concavity

Nov 18, 2022, 11:30 AM
45m
Université Claude Bernard Lyon I, campus de la Doua.

Université Claude Bernard Lyon I, campus de la Doua.

Bâtiment Braconnier Mail Claude Bernard Villeurbanne

Speaker

Boris Thibert

Description

The stability of optimal transport maps under variation of the measures is fundamental from a mathematical viewpoint and is for instance closely related to the convergence of numerical approaches to solve optimal transport problems.

In this talk, I will first introduce the notion of strong $c$-concavity and show that it plays an important role for proving stability results in optimal transport for general cost functions $c$. I will then introduce a differential criterion for proving that a function is strongly $c$-concave, under the assumption that the cost $c$ satisfies the classical Ma-Trudinger-Wang condition that appears in the regularity theory of optimal transport. I will finally show applications to the reflector problem and the Gaussian curvature measure prescription problem. This a joint work with Anatole Gallouet and Quentin Mérigot.

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