Metric extrapolation in the Wasserstein space

Gallouët, Thomas; Natale, Andrea; Todeschi, Gabriele

Type de document :

Pré-publication ou Document de travail

Titre :

Metric extrapolation in the Wasserstein space

Auteur(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

Mot(s)-clé(s) en anglais :

Toland duality
Wasserstein space
Weak optimal transport
Convex order

Discipline(s) HAL :

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

Résumé en anglais : [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 ...
Lire la suite >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.Lire moins >

Langue :

Anglais

Projet ANR :

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

Collections :