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Russian Mathematical Surveys, 2012, Volume 67, Issue 5, Pages 785–890
DOI: https://doi.org/10.1070/RM2012v067n05ABEH004808 (Mi rm9490) 		 
This article is cited in 135 scientific papers (total in 136 papers)

The Monge–Kantorovich problem: achievements, connections, and perspectives

V. I. Bogachevab, A. V. Kolesnikovc

a M. V. Lomonosov Moscow State University
b St. Tikhon's Orthodox University
c Higher School of Economics
English version PDF (1291 kB) Citations (136)
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DOI: https://doi.org/10.1070/RM2012v067n05ABEH004808
Abstract: 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, optimal transportation, transport inequality, Kantorovich–Rubinshtein metric.
Received: 20.06.2012
Russian version:
Uspekhi Matematicheskikh Nauk, 2012, Volume 67, Issue 5(407), Pages 3–110
DOI: https://doi.org/10.4213/rm9490
Bibliographic databases:
Document Type: Article
UDC: 519.2+517.9
MSC: 28C20, 35J96, 49Q20, 60B05
Language: English
Original paper language: Russian
Citation: V. I. Bogachev, A. V. Kolesnikov, “The Monge–Kantorovich problem: achievements, connections, and perspectives”, Uspekhi Mat. Nauk, 67:5(407) (2012), 3–110; Russian Math. Surveys, 67:5 (2012), 785–890
Citation in format AMSBIB
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    • This publication is cited in the following 136 articles:
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    Russian version PDF:2289
    English version PDF:171
    References:192
    First page:136
     
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