# 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

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topBeiglböck, 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/222460>.

@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; optimal transport; Fenchel's perturbation technique},

language = {eng},

month = {7},

pages = {306-323},

publisher = {EDP Sciences},

title = {A generalized dual maximizer for the Monge–Kantorovich transport problem∗},

url = {http://eudml.org/doc/222460},

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

DA - 2012/7//

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; optimal transport; Fenchel's perturbation technique

UR - http://eudml.org/doc/222460

ER -

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