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From Knothe's transport to Brenier's map and a continuation method for optimal transport

dc.contributor.authorSantambrogio, Filippo
hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorCarlier, Guillaume
dc.contributor.authorGalichon, Alfred
dc.date.accessioned2010-02-15T13:09:46Z
dc.date.available2010-02-15T13:09:46Z
dc.date.issued2010
dc.identifier.issn0036-1410
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/3462
dc.language.isoenen
dc.subjectcontinuation methods
dc.subjectoptimal transport
dc.subjectrearrangement of vector-valued maps
dc.subjectKnothe-Rosenblatt transport
dc.subject.ddc519en
dc.titleFrom Knothe's transport to Brenier's map and a continuation method for optimal transport
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenA simple procedure to map two probability measures in R^d is the so-called Knothe-Rosenblatt rearrangement, which consists in rearranging monotonically the marginal distributions of the first coordinate, and then the conditional distributions, iteratively. We show that this mapping is the limit of solutions to a class of Monge-Kantorovich mass transportation problems with quadratic costs, with the weights of the coordinates asymptotically dominating one another. This enables us to design a continuation method for numerically solving the optimal transport problem.
dc.relation.isversionofjnlnameSIAM Journal on Mathematical Analysis
dc.relation.isversionofjnlvol41
dc.relation.isversionofjnlissue6
dc.relation.isversionofjnldate2010
dc.relation.isversionofjnlpages2554-2576
dc.relation.isversionofdoihttp://dx.doi.org/10.1137/080740647
dc.description.sponsorshipprivateouien
dc.relation.isversionofjnlpublisherSIAM - Society for Industrial and Applied Mathematics
dc.subject.ddclabelProbabilités et mathématiques appliquéesen
dc.description.ssrncandidatenon
dc.description.halcandidateoui
dc.description.readershiprecherche
dc.description.audienceInternational
dc.relation.Isversionofjnlpeerreviewedoui
dc.date.updated2022-11-25T08:55:26Z
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