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The Nonlinear Kantorovich Transportation Problem with Nonconvex Costs

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Functional Analysis and Its Applications Aims and scope

Abstract

The paper is devoted to the study of the Kantorovich optimal transportation problem with nonlinear cost functional generated by a cost function depending on the conditional measures of the transport plan. The case of a cost function nonconvex in the second argument is considered. It is proved that this nonlinear Kantorovich problem with general cost function on a Souslin space can be reduced to the same problem with a convex cost function.

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Funding

This research was supported by the Russian Science Foundation grant no. 22-11-00015 and performed at the Lomonosov Moscow State University. The author is a holder of scholarship of the Theoretical Physics and Mathematics Advancement Foundation “BASIS.”

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Authors and Affiliations

  1. Department of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia

    K. A. Afonin

  2. Moscow Center for Fundamental and Applied Mathematics, Moscow, Russia

    K. A. Afonin

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  1. K. A. Afonin
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Correspondence to K. A. Afonin.

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The author of this work declares that he has no conflicts of interest.

Additional information

Translated from Funktsional'nyi Analiz i ego Prilozheniya, 2023, Vol. 57, pp. 3–16 https://doi.org/10.4213/faa4124.

Dedicated to the 110th birthday of Israel Moiseevich Gelfand

Translated by K. A. Afonin

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Afonin, K.A. The Nonlinear Kantorovich Transportation Problem with Nonconvex Costs. Funct Anal Its Appl 57, 267–278 (2023). https://doi.org/10.1134/S0016266323040019

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  • DOI: https://doi.org/10.1134/S0016266323040019

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