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

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dc.creatorCarlier, Guillaume
dc.creatorGalichon, Alfred
dc.creatorSantambrogio, Filippo
dc.date2008-10-22
dc.date.accessioned2026-07-07T10:12:38Z
dc.date.available2026-07-07T10:12:38Z
dc.descriptionA simple procedure to map two probability measures in $\mathbb{R}^d$ is the so-called \emph{Knothe-Rosenblatt rearrangement}, which consists in rearranging monotonically the marginal distributions of the last 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.identifierhttps://arxiv.org/abs/0810.4153
dc.identifierhttp://arxiv.org/abs/0810.4153
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/172247
dc.subjectOptimization and Control
dc.subject49J40
dc.titleFrom Knothe's transport to Brenier's map and a continuation method for optimal transport
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