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

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

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

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topLéonard, 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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