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Matematicheskie Zametki, 2022, Volume 112, Issue 3, Pages 360–370
DOI: https://doi.org/10.4213/mzm13545 (Mi mzm13545) 		 
This article is cited in 7 scientific papers (total in 7 papers)

Existence of Solutions to the Nonlinear Kantorovich Transportation Problem

V. I. Bogachevabcd, A. V. Rezbayevb

a Lomonosov Moscow State University
b National Research University "Higher School of Economics", Moscow
c St. Tikhon's Orthodox University, Moscow
d Moscow Center for Fundamental and Applied Mathematics
Full-text PDF (489 kB) Citations (7)
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DOI: https://doi.org/10.4213/mzm13545
Abstract: We study the existence of solutions to the Kantorovich optimal transportation problem with a nonlinear cost functional generated by a cost function depending on the transport plan. We also consider the case of a cost function depending on the conditional measures of the transport plan. Broad sufficient conditions are obtained for the existence of optimal plans for Radon marginal distributions on completely regular spaces and a lower semicontinuous cost function.
Keywords: Kantorovich problem, conditional measure, nonlinear cost functional, cost function.
Funding agency Grant number
Russian Foundation for Basic Research 20-01-00432
Ministry of Science and Higher Education of the Russian Federation 075-15-2022-284
Foundation for the Development of Science, Education and Family "Living Tradition"
This work was supported by the Russian Foundation for Basic Research under grant 20-01-00432, the project “Kantorovich's parametric problem of optimal transportation”, with the support of PSTGU and the “Living Tradition” foundation, and also supported by the Ministry of Education and Science of the Russian Federation as part of the program of the Moscow Center for Fundamental and Applied Mathematics under the agreement No. 075-15-2022-284 (results in Sec. 2).
Received: 14.04.2022
English version:
Mathematical Notes, 2022, Volume 112, Issue 3, Pages 369–377
DOI: https://doi.org/10.1134/S0001434622090048
Bibliographic databases:
Document Type: Article
UDC: 517.97+517.987+517.988.3
Language: Russian
Citation: V. I. Bogachev, A. V. Rezbayev, “Existence of Solutions to the Nonlinear Kantorovich Transportation Problem”, Mat. Zametki, 112:3 (2022), 360–370; Math. Notes, 112:3 (2022), 369–377
Citation in format AMSBIB
\Bibitem{BogRez22}
\by V.~I.~Bogachev, A.~V.~Rezbayev
\paper Existence of Solutions to the Nonlinear Kantorovich Transportation Problem
\jour Mat. Zametki
\yr 2022
\vol 112
\issue 3
\pages 360--370
\mathnet{http://mi.mathnet.ru/mzm13545}
\crossref{https://doi.org/10.4213/mzm13545}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4538772}
\transl
\jour Math. Notes
\yr 2022
\vol 112
\issue 3
\pages 369--377
\crossref{https://doi.org/10.1134/S0001434622090048}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85140612472}
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  • https://doi.org/10.4213/mzm13545
  • https://www.mathnet.ru/eng/mzm/v112/i3/p360
    • This publication is cited in the following 7 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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