On nonlinear Kantorovich problems for cost functions of a special form

2022/12/20 by Svetlana Popova, Popova, Svetlana
Mathematics · #Differential Equations and Boundary Problems #FOS: Mathematics #Functional Analysis (math.FA) #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.2212.10473

openalex publication_date 2022/12/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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