Geodesic
The Monge--Kantorovich problem: achievements, connections, and perspectives
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 67 (2012) no. 5, pp. 785-890

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This article gives a survey of recent research related to the Monge–Kantorovich problem. Principle results are presented on the existence of solutions and their properties both in the Monge optimal transportation problem and the Kantorovich optimal plan problem, along with results on the connections between both problems and the cases when they are equivalent. Diverse applications of these problems in non-linear analysis, probability theory, and differential geometry are discussed. Bibliography: 196 titles.
Keywords: Monge problem, Kantorovich problem, transport inequality, Kantorovich–Rubinshtein metric.
Mots-clés : optimal transportation 
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V. I. Bogachev; A. V. Kolesnikov. The Monge--Kantorovich problem: achievements, connections, and perspectives. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 67 (2012) no. 5, pp. 785-890. http://geodesic.mathdoc.fr/item/RM_2012_67_5_a0/