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Journal articles
From Knothe’s transport to Brenier’s map and a continuation method for optimal transport
Abstract : A simple procedure to map two probability measures in ℝd 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.
https://hal-sciencespo.archives-ouvertes.fr/hal-03473711
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Submitted on : Thursday, December 9, 2021 - 11:56:54 PM
Last modification on : Friday, March 25, 2022 - 3:57:51 AM
Contributor : Spire Sciences Po Institutional Repository Connect in order to contact the contributor
Submitted on : Thursday, December 9, 2021 - 11:56:54 PM
Last modification on : Friday, March 25, 2022 - 3:57:51 AM
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