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:XZ and t:YZ 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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     publisher = {EDP-Sciences},
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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://archive.numdam.org/articles/10.1051/cocv:2004034/

[1] Y. Brenier, Polar factorization and monotone rearrangements of vector-valued functions. Comm. Pure App. Math. 44 (1991) 375-417. | Zbl

[2] G. Carlier, Duality and existence for a class of mass transportation problems and economic applications, Adv. Math. Economics 5 (2003) 1-21.

[3] I. Ekeland and R. Temam, Convex analysis and variational problems. North-Holland Elsevier (1974) new edition, SIAM Classics in Appl. Math. (1999). | MR | Zbl

[4] W. Gangbo and R. Mccann, The geometry of optimal transportation. Acta Math. 177 (1996) 113-161. | Zbl

[5] I. Ekeland, J. Heckman and L. Nesheim, Identification and estimation of hedonic models. J. Political Economy 112 (2004) 60-109.

[6] L. Kantorovitch, On the transfer of masses, Dokl. Ak. Nauk USSR 37 (1942) 7-8.

[7] S. Rachev and A. Ruschendorf, Mass transportation problems. Springer-Verlag (1998).

[8] C. Villani, Topics in mass transportation. Grad. Stud. Math. 58 (2003) | MR | Zbl

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