Metric extrapolation in the Wasserstein space

Gallouët, Thomas; Natale, Andrea; Todeschi, Gabriele

Document type :

Pré-publication ou Document de travail

Title :

Metric extrapolation in the Wasserstein space

Author(s) :

Gallouët, Thomas [Auteur]
Méthodes particulaires utilisant Monge-Ampère [PARMA]
Natale, Andrea [Auteur]
Laboratoire Paul Painlevé - UMR 8524 [LPP]
Reliable numerical approximations of dissipative systems [RAPSODI]
Todeschi, Gabriele [Auteur]
Université Gustave Eiffel

English keyword(s) :

Toland duality
Wasserstein space
Weak optimal transport
Convex order

HAL domain(s) :

Mathématiques [math]/Optimisation et contrôle [math.OC]

English abstract : [en]

In this article we study a variational problem providing a way to extend for all times minimizing geodesics connecting two given probability measures, in the Wasserstein space. This is simply obtained by allowing for ...
Show more >In this article we study a variational problem providing a way to extend for all times minimizing geodesics connecting two given probability measures, in the Wasserstein space. This is simply obtained by allowing for negative coefficients in the classical variational characterization of Wasserstein barycenters. We show that this problem admits two equivalent convex formulations: the first can be seen as a particular instance of Toland duality and the second is a barycentric optimal transport problem. We propose an efficient numerical scheme to solve this latter formulation based on entropic regularization and a variant of Sinkhorn algorithm.Show less >

Language :

Anglais

ANR Project :

Centre Européen pour les Mathématiques, la Physique et leurs Interactions
Models and algorithms: from the discrete to the continuous

Collections :