Optimal transportation theory with repulsive costs
Di Marino, Simone; Gerolin, Augusto; Nenna, Luca (2017), Optimal transportation theory with repulsive costs, in Filippo Santambrogio, Thierry Champion, Guillaume Carlier, Martin Rumpf, Édouard Oudet, Maïtine Bergounioux, Topological Optimization and Optimal Transport, De Gruyter, p. 204-256
External document linkhttps://hal.inria.fr/hal-01163737
Book titleTopological Optimization and Optimal Transport
Book authorFilippo Santambrogio, Thierry Champion, Guillaume Carlier, Martin Rumpf, Édouard Oudet, Maïtine Bergounioux
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Abstract (EN)This survey intents to present the state of art and recent developments of the optimal transportation theory with many marginals for a class of repulsive cost functions.We introduce some aspects of the Density Functional Theory (DFT) from a mathematical viewpoint, and revisit the theory of optimal transport from its perspective. Moreover, in the last three sections, we describe some recent and new theoretical and numerical results obtained for the Coulomb cost, the repulsive harmonic cost and the determinant.
Subjects / Keywordstranqportation theory; Density Functional Theory
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Seidl, Michael; Marino, Simone; Gerolin, Augusto; Nenna, Luca; Giesbertz, Klaas; Gori-Giorgi, Paola (2017) Document de travail / Working paper