Afficher la notice abrégée

dc.contributor.authorBenamou, Jean-David
dc.contributor.authorCarlier, Guillaume
dc.contributor.authorCuturi, Marco
dc.contributor.authorNenna, Luca
dc.contributor.authorPeyré, Gabriel
dc.date.accessioned2015-02-27T10:29:53Z
dc.date.available2015-02-27T10:29:53Z
dc.date.issued2015
dc.identifier.issn1064-8275
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/14715
dc.language.isoenen
dc.subjectKullback-Leibler Bregman divergence projection
dc.subjectTransportation Problems
dc.subjectIterative Bregman Projections
dc.subject.ddc515en
dc.titleIterative Bregman Projections for Regularized Transportation Problems
dc.typeArticle accepté pour publication ou publié
dc.contributor.editoruniversityotherKyoto University;Japon
dc.contributor.editoruniversityotherINRIA Paris-Rocquencourt - MOKAPLAN;France
dc.description.abstractenThis article details a general numerical framework to approximate so-lutions to linear programs related to optimal transport. The general idea is to introduce an entropic regularization of the initial linear program. This regularized problem corresponds to a Kullback-Leibler Bregman di-vergence projection of a vector (representing some initial joint distribu-tion) on the polytope of constraints. We show that for many problems related to optimal transport, the set of linear constraints can be split in an intersection of a few simple constraints, for which the projections can be computed in closed form. This allows us to make use of iterative Bregman projections (when there are only equality constraints) or more generally Bregman-Dykstra iterations (when inequality constraints are in-volved). We illustrate the usefulness of this approach to several variational problems related to optimal transport: barycenters for the optimal trans-port metric, tomographic reconstruction, multi-marginal optimal trans-port and in particular its application to Brenier's relaxed solutions of in-compressible Euler equations, partial un-balanced optimal transport and optimal transport with capacity constraints.
dc.publisher.cityParisen
dc.relation.isversionofjnlnameSIAM Journal on Scientific Computing
dc.relation.isversionofjnlvol37
dc.relation.isversionofjnlissue2
dc.relation.isversionofjnldate2015
dc.relation.isversionofjnlpagesA1111–A1138
dc.relation.isversionofdoi10.1137/141000439
dc.identifier.urlsitehttps://arxiv.org/abs/1412.5154v1
dc.relation.isversionofjnlpublisherSIAM - Society for Industrial and Applied Mathematics
dc.subject.ddclabelAnalyseen
dc.description.submittednonen
dc.description.ssrncandidatenon
dc.description.halcandidateoui
dc.description.readershiprecherche
dc.description.audienceInternational
dc.relation.Isversionofjnlpeerreviewedoui
dc.date.updated2018-04-13T08:16:54Z


Fichiers attachés à cette notice

FichiersTailleFormatConsulter

Il n'y a pas de fichiers associés à cette notice.

Ce document fait partie de la (des) collection(s) suivante(s)

Afficher la notice abrégée