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dc.contributor.authorCarlier, Guillaume
dc.contributor.authorDuval, Vincent
HAL ID: 7243
ORCID: 0000-0002-7709-256X
dc.contributor.authorPeyré, Gabriel
HAL ID: 1211
dc.contributor.authorSchmitzer, Bernhard
dc.date.accessioned2017-11-03T10:39:16Z
dc.date.available2017-11-03T10:39:16Z
dc.date.issued2017
dc.identifier.issn0036-1410
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/16906
dc.language.isoenen
dc.subjectOptimal transport
dc.subjectgradient flows
dc.subjectentropic regularization
dc.subject.ddc515en
dc.titleConvergence of Entropic Schemes for Optimal Transport and Gradient Flows
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenReplacing positivity constraints by an entropy barrier is popular to approximate solutions of linear programs. In the special case of the optimal transport problem, this technique dates back to the early work of Schr\odinger. This approach has recently been used successfully to solve optimal transport related problems in several applied fields such as imaging sciences, machine learning and social sciences. The main reason for this success is that, in contrast to linear programming solvers, the resulting algorithms are highly parallelizable and take advantage of the geometry of the computational grid (e.g. an image or a triangulated mesh). The first contribution of this article is the proof of the Γ-convergence of the entropic regularized optimal transport problem towards the Monge-Kantorovich problem for the squared Euclidean norm cost function. This implies in particular the convergence of the optimal entropic regularized transport plan towards an optimal transport plan as the entropy vanishes. Optimal transport distances are also useful to define gradient flows as a limit of implicit Euler steps according to the transportation distance. Our second contribution is a proof that implicit steps according to the entropic regularized distance converge towards the original gradient flow when both the step size and the entropic penalty vanish (in some controlled way)."
dc.relation.isversionofjnlnameSIAM Journal on Mathematical Analysis
dc.relation.isversionofjnlvol49
dc.relation.isversionofjnlissue2
dc.relation.isversionofjnldate2017
dc.relation.isversionofjnlpages1385-1418
dc.relation.isversionofdoi10.1137/15M1050264
dc.identifier.urlsitehttps://arxiv.org/abs/1512.02783
dc.relation.isversionofjnlpublisherSIAM - Society for Industrial and Applied Mathematics
dc.subject.ddclabelAnalyseen
dc.description.ssrncandidatenon
dc.description.halcandidatenon
dc.description.readershiprecherche
dc.description.audienceInternational
dc.relation.Isversionofjnlpeerreviewedoui
dc.date.updated2018-04-13T08:28:30Z


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