A Numerical Method to Solve Multi-Marginal Optimal Transport Problems with Coulomb Cost
Benamou, Jean-David; Carlier, Guillaume; Nenna, Luca (2017), A Numerical Method to Solve Multi-Marginal Optimal Transport Problems with Coulomb Cost, in Glowinski R., Osher S., Yin W., Splitting Methods in Communication, Imaging, Science, and Engineering, Springer : Berlin Heidelberg, p. 577-601. https://doi.org/10.1007/978-3-319-41589-5_17
External document linkhttps://hal.inria.fr/hal-01148954
Book titleSplitting Methods in Communication, Imaging, Science, and Engineering
Book authorGlowinski R., Osher S., Yin W.
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Abstract (EN)In this chapter, 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.
Subjects / Keywordscoulomb cost
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Benamou, Jean-David; Carlier, Guillaume; Cuturi, Marco; Nenna, Luca; Peyré, Gabriel (2015) Article accepté pour publication ou publié