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hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorChizat, Lénaïc
HAL ID: 19586
*
hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorPeyré, Gabriel
HAL ID: 1211
*
hal.structure.identifierInstitute for Computational and Applied Mathematics [Münster] [Numerische und Angewandte Mathematik]
hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorSchmitzer, Bernhard*
hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorVialard, François-Xavier*
dc.date.accessioned2018-01-15T15:44:22Z
dc.date.available2018-01-15T15:44:22Z
dc.date.issued2018
dc.identifier.issn0025-5718
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/17348
dc.language.isoenen
dc.subjectunbalanced optimal transporten
dc.subject.ddc510en
dc.titleScaling Algorithms for Unbalanced Transport Problemsen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenThis article introduces a new class of fast algorithms to approx-imate variational problems involving unbalanced optimal transport. While classical optimal transport considers only normalized probability distributions, it is important for many applications to be able to compute some sort of re-laxed transportation between arbitrary positive measures. A generic class of such “unbalanced” optimal transport problems has been recently proposed by several authors. In this paper, we show how to extend the, now classical, entropic regularization scheme to these unbalanced problems. This gives rise to fast, highly parallelizable algorithms that operate by performing only diagonal scaling (i.e. pointwise multiplications) of the transportation couplings. They are generalizations of the celebrated Sinkhorn algorithm. We show how these methods can be used to solve unbalanced transport, unbalanced gradient flows, and to compute unbalanced barycenters. We showcase applications to 2-D shape modification, color transfer, and growth models.en
dc.relation.isversionofjnlnameMathematics of Computation
dc.relation.isversionofjnlvol87
dc.relation.isversionofjnldate2018
dc.relation.isversionofjnlpages2563-2609en
dc.relation.isversionofdoi10.1090/mcom/3303en
dc.identifier.urlsitehttps://hal.archives-ouvertes.fr/hal-01434914en
dc.relation.isversionofjnlpublisherNational Academy of Sciences-National Research Councilen
dc.subject.ddclabelMathématiquesen
dc.description.ssrncandidatenonen
dc.description.halcandidatenonen
dc.description.readershiprechercheen
dc.description.audienceInternationalen
dc.relation.Isversionofjnlpeerreviewedouien
dc.relation.Isversionofjnlpeerreviewedouien
dc.date.updated2018-01-15T15:32:58Z
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