# An optimal matching problem

ESAIM: Control, Optimisation and Calculus of Variations (2010)

- Volume: 11, Issue: 1, page 57-71
- ISSN: 1292-8119

## Access Full Article

top## Abstract

top## How to cite

topEkeland, Ivar. "An optimal matching problem." ESAIM: Control, Optimisation and Calculus of Variations 11.1 (2010): 57-71. <http://eudml.org/doc/90756>.

@article{Ekeland2010,

abstract = {
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 $s:X\rightarrow Z$ and $t:Y\rightarrow Z$ such that the images $s(\mu)$
and $t(\nu)$ coincide, and the integral $\int_\{X\}u(x,s(x))d\mu-\int
_\{Y\}v(y,t(y))d\nu$ is maximal. We give condition on u and v for which
there is a unique solution.
},

author = {Ekeland, Ivar},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {optimal transportation; measure-preserving maps.; measure-preserving maps},

language = {eng},

month = {3},

number = {1},

pages = {57-71},

publisher = {EDP Sciences},

title = {An optimal matching problem},

url = {http://eudml.org/doc/90756},

volume = {11},

year = {2010},

}

TY - JOUR

AU - Ekeland, Ivar

TI - An optimal matching problem

JO - ESAIM: Control, Optimisation and Calculus of Variations

DA - 2010/3//

PB - EDP Sciences

VL - 11

IS - 1

SP - 57

EP - 71

AB -
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 $s:X\rightarrow Z$ and $t:Y\rightarrow Z$ such that the images $s(\mu)$
and $t(\nu)$ coincide, and the integral $\int_{X}u(x,s(x))d\mu-\int
_{Y}v(y,t(y))d\nu$ is maximal. We give condition on u and v for which
there is a unique solution.

LA - eng

KW - optimal transportation; measure-preserving maps.; measure-preserving maps

UR - http://eudml.org/doc/90756

ER -

## References

top- Y. Brenier, Polar factorization and monotone rearrangements of vector-valued functions. Comm. Pure App. Math.44 (1991) 375–417.
- G. Carlier, Duality and existence for a class of mass transportation problems and economic applications, Adv. Math. Economics5 (2003) 1–21.
- I. Ekeland and R. Temam, Convex analysis and variational problems. North-Holland Elsevier (1974) new edition, SIAM Classics in Appl. Math. (1999).
- W. Gangbo and R. McCann, The geometry of optimal transportation. Acta Math.177 (1996) 113–161.
- I. Ekeland, J. Heckman and L. Nesheim, Identification and estimation of hedonic models. J. Political Economy112 (2004) 60–109.
- L. Kantorovitch, On the transfer of masses, Dokl. Ak. Nauk USSR37 (1942) 7–8.
- S. Rachev and A. Ruschendorf, Mass transportation problems. Springer-Verlag (1998).
- C. Villani, Topics in mass transportation. Grad. Stud. Math.58 (2003)

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.