An optimal matching problem
ESAIM: Control, Optimisation and Calculus of Variations (2010)
- Volume: 11, Issue: 1, page 57-71
- ISSN: 1292-8119
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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
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- I. Ekeland, J. Heckman and L. Nesheim, Identification and estimation of hedonic models. J. Political Economy112 (2004) 60–109.
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- C. Villani, Topics in mass transportation. Grad. Stud. Math.58 (2003)
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