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An augmented Lagrangian approach to Wasserstein gradient flows and applications

dc.contributor.authorBenamou, Jean-David
dc.contributor.authorCarlier, Guillaume
dc.contributor.authorLaborde, Maxime
dc.date.accessioned2017-11-03T10:56:41Z
dc.date.available2017-11-03T10:56:41Z
dc.date.issued2016
dc.identifier.issn2267-3059
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/16907
dc.language.isoenen
dc.subjectBenamou-Brenier formulation
dc.subjectaugmented Lagrangian
dc.subjectnon-linear diffusion
dc.subjectgranular media
dc.subjectsystems
dc.subjectcrowd motions
dc.subjectWasserstein gradi-ent flows
dc.subject.ddc515en
dc.titleAn augmented Lagrangian approach to Wasserstein gradient flows and applications
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenTaking 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.
dc.relation.isversionofjnlnameESAIM: Proceedings and Surveys
dc.relation.isversionofjnlvol54
dc.relation.isversionofjnldate2016
dc.relation.isversionofjnlpages1-17
dc.relation.isversionofdoi10.1051/proc/201654001
dc.identifier.urlsitehttps://hal.archives-ouvertes.fr/hal-01245184
dc.relation.isversionofjnlpublisherEDP Sciences
dc.subject.ddclabelAnalyseen
dc.description.ssrncandidatenon
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dc.description.readershiprecherche
dc.description.audienceInternational
dc.relation.Isversionofjnlpeerreviewedoui
dc.date.updated2018-04-13T08:24:33Z


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