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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

Type
Chapitre d'ouvrage
External document link
https://hal.inria.fr/hal-01163737
Date
2017
Book title
Topological Optimization and Optimal Transport
Book author
Filippo Santambrogio, Thierry Champion, Guillaume Carlier, Martin Rumpf, Édouard Oudet, Maïtine Bergounioux
Publisher
De Gruyter
ISBN
9783110430509
Pages
204-256
Metadata
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Author(s)
Di Marino, Simone
Gerolin, Augusto
Nenna, Luca
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 / Keywords
tranqportation theory; Density Functional Theory