An optimal matching problem

Ekeland, Ivar 

ESAIM: Control, Optimisation and Calculus of Variations, Tome 11 (2005) no. 1, pp. 57-71

Résumé

Given two measured spaces $(X,\mu )$ and $(Y,\nu )$, and a third space $Z$, given two functions $u(x,z)$ and $v(x,z)$, we study the problem of finding two maps $s:X\to Z$ and $t:Y\to Z$ such that the images $s\left(\mu \right)$ and $t\left(\nu \right)$ coincide, and the integral ${\int }_{X}u(x,s\left(x\right))d\mu -{\int }_{Y}v(y,t\left(y\right))d\nu$ is maximal. We give condition on $u$ and $v$ for which there is a unique solution.

Détail

DOI : 10.1051/cocv:2004034

Classification : 05C38, 15A15, 05A15, 15A18
Keywords: optimal transportation, measure-preserving maps