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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)
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.
Received: 18.03.2023
Citation:
S. N. Popova, “On nonlinear Kantorovich problems for cost functions of a special form”, Algebra i Analiz, 36:4 (2024), 165–194
Linking options:
https://www.mathnet.ru/eng/aa1931 https://www.mathnet.ru/eng/aa/v36/i4/p165
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Statistics & downloads: |
Abstract page: | 194 | Full-text PDF : | 3 | References: | 31 | First page: | 18 |
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