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dc.contributor.authorDuval, Vincent
dc.contributor.authorBenamou, Jean-David
dc.date.accessioned2019-09-24T12:40:19Z
dc.date.available2019-09-24T12:40:19Z
dc.date.issued2018
dc.identifier.issn0956-7925
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/19907
dc.language.isoenen
dc.subjectOptimal transporten
dc.subjectMonge-Ampère equationen
dc.subjectfinite-difference schemeen
dc.subject.ddc515en
dc.titleMinimal convex extensions and finite difference discretisation of the quadratic Monge–Kantorovich problemen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenWe present an adaptation of the Monge–Ampère (MA) lattice basis reduction scheme to the MA equation with second boundary value condition, provided the target is a convex set. This yields a fast adaptive method to numerically solve the optimal transport (OT) problem between two absolutely continuous measures, the second of which has convex support. The proposed numerical method actually captures a specific Brenier solution which is minimal in some sense. We prove the convergence of the method as the grid step size vanishes and show with numerical experiments that it is able to reproduce subtle properties of the OT problem.en
dc.relation.isversionofjnlnameEuropean Journal of Applied Mathematics
dc.relation.isversionofjnldate2018-09
dc.relation.isversionofjnlpages1-38en
dc.relation.isversionofdoi10.1017/S0956792518000451en
dc.relation.isversionofjnlpublisherCambridge University Pressen
dc.subject.ddclabelAnalyseen
dc.relation.forthcomingnonen
dc.relation.forthcomingprintnonen
dc.description.ssrncandidatenonen
dc.description.halcandidatenonen
dc.description.readershiprechercheen
dc.description.audienceInternationalen
dc.relation.Isversionofjnlpeerreviewedouien
dc.relation.Isversionofjnlpeerreviewedouien
dc.date.updated2019-09-24T12:38:26Z
hal.person.labIds60
hal.person.labIds60


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