The Nonlinear Kantorovich Transportation Problem with Nonconvex Costs

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 t...

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Bibliographic Details
Published inFunctional analysis and its applications Vol. 57; no. 4; pp. 267 - 278
Main Author Afonin, K. A.
Format Journal Article
LanguageEnglish
Published Moscow Pleiades Publishing 01.12.2023
Springer Nature B.V
Subjects
14/34
639/766/189
639/766/530
639/766/747
Analysis
Cost function
Functional Analysis
Mathematics
Mathematics and Statistics
Transportation planning
Transportation problem
cost function
Kantorovich problem
conditional measure
nonlinear cost functional
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Summary: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.
ISSN:0016-2663
1573-8485
DOI:10.1134/S0016266323040019