Geodesic
An augmented Lagrangian approach to Wasserstein gradient flows and applications
Jean-David Benamou1 ; Guillaume Carlier2 ; Maxime Laborde2
1 INRIA Paris, MOKAPLAN, rue Simone Iff, 75012, Paris, FRANCE and CEREMADE
2 CEREMADE, UMR CNRS 7534, Université Paris IX Dauphine, Pl. de Lattre de Tassigny, 75775 Paris Cedex 16, FRANCE and MOKAPLAN
ESAIM. Proceedings, Tome 54 (2016), pp. 1-17.

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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.
DOI : 10.1051/proc/201654001

Jean-David Benamou 1 ; Guillaume Carlier 2 ; Maxime Laborde 2

1 INRIA Paris, MOKAPLAN, rue Simone Iff, 75012, Paris, FRANCE and CEREMADE
2 CEREMADE, UMR CNRS 7534, Université Paris IX Dauphine, Pl. de Lattre de Tassigny, 75775 Paris Cedex 16, FRANCE and MOKAPLAN 
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     title = {An augmented {Lagrangian} approach to {Wasserstein} gradient flows and applications},
     journal = {ESAIM. Proceedings},
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     doi = {10.1051/proc/201654001},
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     url = {http://geodesic.mathdoc.fr/articles/10.1051/proc/201654001/}
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Jean-David Benamou; Guillaume Carlier; Maxime Laborde. An augmented Lagrangian approach to Wasserstein gradient flows and applications. ESAIM. Proceedings, Tome 54 (2016), pp. 1-17. doi : 10.1051/proc/201654001. http://geodesic.mathdoc.fr/articles/10.1051/proc/201654001/

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