Type
Article
Titre
From Knothe's transport to Brenier's map and a continuation method for optimal transport
Dans
SIAM journal on mathematical analysis
Auteur(s)
CARLIER Guillaume - CEntre de REcherches en MAthématiques de la DEcision (Auteur)
GALICHON Alfred - Department of Economics, Ecole Polytechnique (Auteur)
SANTAMBROGIO Filippo - Laboratoire de Mathématiques d'Orsay (Auteur)
Éditeur
US : Society for Industrial and Applied Mathematics
Volume
416
Pages
2554 - 2576 p.
ISSN
00361410
Résumé
EN
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.

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