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Augmented Lagrangian Methods for Transport Optimization, Mean Field Games and Degenerate Elliptic Equations

dc.contributor.authorBenamou, Jean-David
dc.contributor.authorCarlier, Guillaume
dc.date.accessioned2015-04-07T11:45:19Z
dc.date.available2015-04-07T11:45:19Z
dc.date.issued2015
dc.identifier.issn0022-3239
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/14893
dc.language.isoenen
dc.subjectOptimal transport
dc.subjectMean field games
dc.subjectMonge problem
dc.subjectDegenerate elliptic PDEs
dc.subjectAugmented Lagrangian
dc.subject.ddc519en
dc.titleAugmented Lagrangian Methods for Transport Optimization, Mean Field Games and Degenerate Elliptic Equations
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenMany problems from mass transport can be reformulated as variational problems under a prescribed divergence constraint (static problems) or subject to a time-dependent continuity equation, which again can be formulated as a divergence constraint but in time and space. The variational class of mean field games, introduced by Lasry and Lions, may also be interpreted as a generalization of the time-dependent optimal transport problem. Following Benamou and Brenier, we show that augmented Lagrangian methods are well suited to treat such convex but non-smooth problems. They include in particular Monge historic optimal transport problem. A finite-element discretization and implementation of the method are used to provide numerical simulations and a convergence study.
dc.relation.isversionofjnlnameJournal of Optimization Theory and Applications
dc.relation.isversionofjnlvol167
dc.relation.isversionofjnlissue1
dc.relation.isversionofjnldate2015
dc.relation.isversionofjnlpages1-26
dc.relation.isversionofdoihttp://dx.doi.org/10.1007/s10957-015-0725-9
dc.identifier.urlsitehttps://hal.inria.fr/hal-01073143
dc.relation.isversionofjnlpublisherSpringer
dc.subject.ddclabelProbabilités et mathématiques appliquéesen
dc.relation.forthcomingnonen
dc.relation.forthcomingprintouien
dc.description.ssrncandidatenon
dc.description.halcandidateoui
dc.description.readershiprecherche
dc.description.audienceInternational
dc.relation.Isversionofjnlpeerreviewedoui
dc.date.updated2018-04-13T08:16:02Z


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