Optimal transportation theory with repulsive costs

Simone Di Marino (1) , Augusto Gerolin (2) , Luca Nenna (3, 4)

1 LM-Orsay - Laboratoire de Mathématiques d'Orsay
2 Dipartimento di Matematica [Pisa]
3 MOKAPLAN - Méthodes numériques pour le problème de Monge-Kantorovich et Applications en sciences sociales
4 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

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.

Domaines: Analyse numérique [math.NA]; Equations aux dérivées partielles [math.AP]; Physique mathématique [math-ph]; Optimisation et contrôle [math.OC]

Simone Di Marino, Augusto Gerolin, Luca Nenna. Optimal transportation theory with repulsive costs. 2015. ⟨hal-01163737v2⟩