Optimal Partial Mass Transportation and Obstacle Monge-Kantorovich Equation

par Van Thanh Nguyen (Université de Limoges)

vendredi 22 janv. 2016, 10:30 → 11:30 Europe/Paris

XLIM Salle X.203

Optimal transport consists in finding the optimal way of moving one mass distribution to another in such a way to minimize a certain work. The problem was first proposed by Monge in 1781 and then it has been generalized in various directions. In this work, we are interested in the optimal partial transport which is one of variants of optimal transport. More precisely, for Finsler distance costs, we introduce equivalent formulations for the characterization of the optimal transportation based on Kantorovich potential, minimum flow problem and a PDE of obstacle Monge-Kantorovich type. By studying properties of this PDE and its connection to optimal partial transport, this allows us to show the uniqueness of the optimal active regions. They are also used for approximating numerical results via an augmented Lagrangian method.