An augmented Lagrangian approach to Wasserstein gradient flows and applications

Abstract : 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.
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Jean-David Benamou, Guillaume Carlier, Maxime Laborde. An augmented Lagrangian approach to Wasserstein gradient flows and applications. ESAIM: Proceedings and Surveys, EDP Sciences, 2019. ⟨hal-01245184⟩

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