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Uspekhi Mat. Nauk, 2012, Volume 67, Issue 5(407), Pages 3–110 (Mi umn9490)  

This article is cited in 76 scientific papers (total in 76 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

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.

DOI: https://doi.org/10.4213/rm9490

Full text: PDF file (1370 kB)
References: PDF file   HTML file

English version:
Russian Mathematical Surveys, 2012, 67:5, 785–890

Bibliographic databases:

UDC: 519.2+517.9
MSC: 28C20, 35J96, 49Q20, 60B05
Received: 20.06.2012

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

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