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

Given two measured spaces (X,μ) and (Y,ν), 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→Z and t:Y→Z such that the images s(μ) and t(ν) coincide, and the integral ∫ X u(x,s(x))dμ-∫ Y v(y,t(y))dν is maximal. We give condition on u and v for which there is a unique solution.

DOI : 10.1051/cocv:2004034
Classification : 05C38, 15A15, 05A15, 15A18
Mots-clés : optimal transportation, measure-preserving maps 
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Ekeland, Ivar. An optimal matching problem. ESAIM: Control, Optimisation and Calculus of Variations, Tome 11 (2005) no. 1, pp. 57-71. doi : 10.1051/cocv:2004034. http://www.numdam.org/articles/10.1051/cocv:2004034/

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