Calculus of Variations and Geometric Measure Theory
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J. D. Benamou - G. Carlier - L. Nenna

A Numerical Method to solveMulti-Marginal Optimal Transport Problems with Coulomb Cost

created by nenna on 29 Jun 2016
modified on 11 Sep 2017


Published Paper

Inserted: 29 jun 2016
Last Updated: 11 sep 2017

Journal: Splitting Methods in Communication, Imaging, Science, and Engineering
Year: 2015
Doi: 10.1007/978-3-319-41589-5_17
Links: url


In this paper, we present a numerical method, based on iterative Bregman projections, to solve the optimal transport problem with Coulomb cost. This is related to the strong interaction limit of Density Functional Theory. The first idea is to introduce an entropic regularization of the Kantorovich formulation of the Optimal Transport problem. The regularized problem then corresponds to the projection of a vector on the intersection of the constraints with respect to the Kullback-Leibler distance. Iterative Bregman projections on each marginal constraint are explicit which enables us to approximate the optimal transport plan. We validate the numerical method against analytical test cases.


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