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Algebra i Analiz, 2024, Volume 36, Issue 4, Pages 165–194 (Mi aa1931)  
This article is cited in 1 scientific paper (total in 1 paper)

Research Papers

On nonlinear Kantorovich problems for cost functions of a special form

S. N. Popovaabc

a Lomonosov Moscow State University
b National Research University Higher School of Economics, Moscow
c Moscow Institute of Physics and Technology (National Research University)
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Abstract: We study Kantorovich type optimal transportation problems with nonlinear cost functions, including dependence on conditional measures of transport plans. A range of nonlinear Kantorovich problems for cost functions of a special form is considered and results on existence (or non-existence) of optimal solutions are proved. We also establish the connection between the nonlinear Kantorovich problem with the cost function of some special form and the Monge problem with convex dominance.
Keywords: optimal transportation problem, nonlinear Kantorovich problem, Monge problem, conditional measure, convex dominance.
Funding agency Grant number
Russian Science Foundation 22-11-00015
Received: 18.03.2023
English version:
St. Petersburg Mathematical Journal, 2025, Volume 36, Issue 4, Pages 619–639
DOI: https://doi.org/10.1090/spmj/1875
Document Type: Article
Language: Russian
Citation: S. N. Popova, “On nonlinear Kantorovich problems for cost functions of a special form”, Algebra i Analiz, 36:4 (2024), 165–194; St. Petersburg Math. J., 36:4 (2025), 619–639
Citation in format AMSBIB
\Bibitem{Pop24}
\by S.~N.~Popova
\paper On nonlinear Kantorovich problems for cost functions of a special form
\jour Algebra i Analiz
\yr 2024
\vol 36
\issue 4
\pages 165--194
\mathnet{http://mi.mathnet.ru/aa1931}
\transl
\jour St. Petersburg Math. J.
\yr 2025
\vol 36
\issue 4
\pages 619--639
\crossref{https://doi.org/10.1090/spmj/1875}
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    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Алгебра и анализ St. Petersburg Mathematical Journal
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