Numerical solution of the Monge–Kantorovich problem by density lift-up continuation

Afaf Bouharguane 1, 2 Angelo Iollo 2, 1 Lisl Weynans 2, 1
1 MEMPHIS - Modeling Enablers for Multi-PHysics and InteractionS
IMB - Institut de Mathématiques de Bordeaux, Inria Bordeaux - Sud-Ouest
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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https://hal.archives-ouvertes.fr/hal-01250636
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Submitted on : Tuesday, January 5, 2016 - 10:05:43 AM
Last modification on : Monday, May 27, 2019 - 3:50:13 PM

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Afaf Bouharguane, Angelo Iollo, Lisl Weynans. Numerical solution of the Monge–Kantorovich problem by density lift-up continuation. ESAIM: Mathematical Modelling and Numerical Analysis, EDP Sciences, 2015, Special Issue - Optimal Transport, 49 (6), pp.1577 ⟨10.1051/m2an/2015024 ⟩. ⟨hal-01250636⟩

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