A generalized dual maximizer for the Monge–Kantorovich transport problem

Mathias Beiglböck; Christian Léonard; Walter Schachermayer

ESAIM: Probability and Statistics (2012)

  • Volume: 16, page 306-323
  • ISSN: 1292-8100

Abstract

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The dual attainment of the Monge–Kantorovich transport problem is analyzed in a general setting. The spaces X,Y are assumed to be polish and equipped with Borel probability measures μ and ν. The transport cost function c : X × Y →  [0,∞]  is assumed to be Borel measurable. We show that a dual optimizer always exists, provided we interpret it as a projective limit of certain finitely additive measures. Our methods are functional analytic and rely on Fenchel’s perturbation technique.

How to cite

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Beiglböck, Mathias, Léonard, Christian, and Schachermayer, Walter. "A generalized dual maximizer for the Monge–Kantorovich transport problem." ESAIM: Probability and Statistics 16 (2012): 306-323. <http://eudml.org/doc/273608>.

@article{Beiglböck2012,
abstract = {The dual attainment of the Monge–Kantorovich transport problem is analyzed in a general setting. The spaces X,Y are assumed to be polish and equipped with Borel probability measures μ and ν. The transport cost function c : X × Y →  [0,∞]  is assumed to be Borel measurable. We show that a dual optimizer always exists, provided we interpret it as a projective limit of certain finitely additive measures. Our methods are functional analytic and rely on Fenchel’s perturbation technique.},
author = {Beiglböck, Mathias, Léonard, Christian, Schachermayer, Walter},
journal = {ESAIM: Probability and Statistics},
keywords = {optimal transport; duality in function spaces; Fenchel’s perturbation technique; Fenchel's perturbation technique},
language = {eng},
pages = {306-323},
publisher = {EDP-Sciences},
title = {A generalized dual maximizer for the Monge–Kantorovich transport problem},
url = {http://eudml.org/doc/273608},
volume = {16},
year = {2012},
}

TY - JOUR
AU - Beiglböck, Mathias
AU - Léonard, Christian
AU - Schachermayer, Walter
TI - A generalized dual maximizer for the Monge–Kantorovich transport problem
JO - ESAIM: Probability and Statistics
PY - 2012
PB - EDP-Sciences
VL - 16
SP - 306
EP - 323
AB - The dual attainment of the Monge–Kantorovich transport problem is analyzed in a general setting. The spaces X,Y are assumed to be polish and equipped with Borel probability measures μ and ν. The transport cost function c : X × Y →  [0,∞]  is assumed to be Borel measurable. We show that a dual optimizer always exists, provided we interpret it as a projective limit of certain finitely additive measures. Our methods are functional analytic and rely on Fenchel’s perturbation technique.
LA - eng
KW - optimal transport; duality in function spaces; Fenchel’s perturbation technique; Fenchel's perturbation technique
UR - http://eudml.org/doc/273608
ER -

References

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