A saddle-point approach to the Monge-Kantorovich optimal transport problem
نویسندگان
چکیده
منابع مشابه
A saddle-point approach to the Monge-Kantorovich optimal transport problem
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 du...
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In the first part of the paper we briefly decribe the classical problem, raised by Monge in 1781, of optimal transportation of mass. We discuss also Kantorovich’s weak solution of the problem, which leads to general existence results, to a dual formulation, and to necessary and sufficient optimality conditions. In the second part we describe some recent progress on the problem of the existence ...
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• Mathematics Subject Classification: 60E15, 90C40, 49N15 •
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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 meas...
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ژورنال
عنوان ژورنال: ESAIM: Control, Optimisation and Calculus of Variations
سال: 2010
ISSN: 1292-8119,1262-3377
DOI: 10.1051/cocv/2010013