Kantorovich duality for general transport costs and applications
نویسندگان
چکیده
منابع مشابه
A general duality theorem for the Monge-Kantorovich transport problem
The duality theory 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. Our main result states that in this setting there is no duality gap, provided the optimal transport problem is formulated in a suitably r...
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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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ژورنال
عنوان ژورنال: Journal of Functional Analysis
سال: 2017
ISSN: 0022-1236
DOI: 10.1016/j.jfa.2017.08.015