An augmented Lagrangian approach to Wasserstein gradient flows and applications

Benamou, Jean-David; Carlier, Guillaume; Laborde, Maxime

Benamou, Jean-David; Carlier, Guillaume; Laborde, Maxime (2016), An augmented Lagrangian approach to Wasserstein gradient flows and applications, ESAIM: Proceedings and Surveys, 54, p. 1-17. 10.1051/proc/201654001

Type

Article accepté pour publication ou publié

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https://hal.archives-ouvertes.fr/hal-01245184

Date

2016

Nom de la revue

ESAIM: Proceedings and Surveys

Volume

Éditeur

EDP Sciences

Pages

1-17

Résumé (EN)

Taking advantage of the Benamou-Brenier dynamic formulation of optimal transport, we propose a convex formulation for each step of the JKO scheme for Wasserstein gradient flows which can be attacked by an augmented Lagrangian method which we call the ALG2-JKO scheme. We test the algorithm in particular on the porous medium equation. We also consider a semi implicit variant which enables us to treat nonlocal interactions as well as systems of interacting species. Regarding systems, we can also use the ALG2-JKO scheme for the simulation of crowd motion models with several species.

Mots-clés

Benamou-Brenier formulation; augmented Lagrangian; non-linear diffusion; granular media; systems; crowd motions; Wasserstein gradi-ent flows