Geodesic
An augmented Lagrangian approach to Wasserstein gradient flows and applications
Jean-David Benamou1 ; Guillaume Carlier2 ; Maxime Laborde2
1INRIA Paris, MOKAPLAN, rue Simone Iff, 75012, Paris, FRANCE and CEREMADE
2CEREMADE, 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 
@article{EP_2016_54_a1,
     author = {Jean-David Benamou and Guillaume Carlier and Maxime Laborde},
     title = {An augmented {Lagrangian} approach to {Wasserstein} gradient flows and applications},
     journal = {ESAIM. Proceedings},
     pages = {1--17},
     year = {2016},
     volume = {54},
     doi = {10.1051/proc/201654001},
     language = {en},
     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

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