A saddle-point approach to the Monge-Kantorovich optimal transport problem

Christian Léonard

ESAIM: Control, Optimisation and Calculus of Variations (2011)

  • Volume: 17, Issue: 3, page 682-704
  • ISSN: 1292-8119

Abstract

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The Monge-Kantorovich problem is revisited by means of a variant of the saddle-point method without appealing to c-conjugates. A new abstract characterization of the optimal plans is obtained in the case where the cost function takes infinite values. It leads us to new explicit sufficient and necessary optimality conditions. As by-products, we obtain a new proof of the well-known Kantorovich dual equality and an improvement of the convergence of the minimizing sequences.

How to cite

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Léonard, Christian. "A saddle-point approach to the Monge-Kantorovich optimal transport problem." ESAIM: Control, Optimisation and Calculus of Variations 17.3 (2011): 682-704. <http://eudml.org/doc/221937>.

@article{Léonard2011,
abstract = { The Monge-Kantorovich problem is revisited by means of a variant of the saddle-point method without appealing to c-conjugates. A new abstract characterization of the optimal plans is obtained in the case where the cost function takes infinite values. It leads us to new explicit sufficient and necessary optimality conditions. As by-products, we obtain a new proof of the well-known Kantorovich dual equality and an improvement of the convergence of the minimizing sequences. },
author = {Léonard, Christian},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Convex optimization; saddle-point; conjugate duality; optimal transport; convex optimization; optimal transport},
language = {eng},
month = {8},
number = {3},
pages = {682-704},
publisher = {EDP Sciences},
title = {A saddle-point approach to the Monge-Kantorovich optimal transport problem},
url = {http://eudml.org/doc/221937},
volume = {17},
year = {2011},
}

TY - JOUR
AU - Léonard, Christian
TI - A saddle-point approach to the Monge-Kantorovich optimal transport problem
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2011/8//
PB - EDP Sciences
VL - 17
IS - 3
SP - 682
EP - 704
AB - The Monge-Kantorovich problem is revisited by means of a variant of the saddle-point method without appealing to c-conjugates. A new abstract characterization of the optimal plans is obtained in the case where the cost function takes infinite values. It leads us to new explicit sufficient and necessary optimality conditions. As by-products, we obtain a new proof of the well-known Kantorovich dual equality and an improvement of the convergence of the minimizing sequences.
LA - eng
KW - Convex optimization; saddle-point; conjugate duality; optimal transport; convex optimization; optimal transport
UR - http://eudml.org/doc/221937
ER -

References

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