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Numerical solution of the Monge-Kantorovich problem by Picard iterations

Afaf Bouharguane 1, 2 Angelo Iollo 1, 2 Lisl Weynans 2, 1 
2 MC2 - Modélisation, contrôle et calcul
Inria Bordeaux - Sud-Ouest, UB - Université de Bordeaux, CNRS - Centre National de la Recherche Scientifique : UMR5251
Abstract : We present an iterative method to numerically solve the L² Monge-Kantorovich problem. The method is based on a Picard fixed point iteration of the linearized problem. Examples relative to the transport of two-dimensional densities show that the present method can significantly reduce the computational time over existing methods, especially when the Wasserstein distance between the densities is small.
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Submitted on : Friday, February 14, 2014 - 9:39:54 AM
Last modification on : Wednesday, October 26, 2022 - 8:16:25 AM
Long-term archiving on: : Thursday, May 15, 2014 - 10:05:29 AM


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  • HAL Id : hal-00946252, version 1



Afaf Bouharguane, Angelo Iollo, Lisl Weynans. Numerical solution of the Monge-Kantorovich problem by Picard iterations. [Research Report] RR-8477, INRIA. 2014. ⟨hal-00946252⟩



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