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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 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.
Littérature citée [11 références]
https://hal-sciencespo.archives-ouvertes.fr/hal-01023796
Contributeur : Spire Sciences Po Institutional Repository <>
Soumis le : mardi 15 juillet 2014 - 11:35:47
Dernière modification le : mardi 6 juillet 2021 - 03:39:50
Contributeur : Spire Sciences Po Institutional Repository <>
Soumis le : mardi 15 juillet 2014 - 11:35:47
Dernière modification le : mardi 6 juillet 2021 - 03:39:50
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knothe-brenier-final.pdf
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