Existence of solutions to the nonlinear Kantorovich transportation problem. (English. Russian original) Zbl 1504.49062
Math. Notes 112, No. 3, 369-377 (2022); translation from Mat. Zametki 112, No. 3, 360-370 (2022).
Summary: We study the existence of solutions to the Kantorovich optimal transportation problem with a nonlinear cost functional generated by a cost function depending on the transport plan. We also consider the case of a cost function depending on the conditional measures of the transport plan. Broad sufficient conditions are obtained for the existence of optimal plans for Radon marginal distributions on completely regular spaces and a lower semicontinuous cost function.
MSC:
| 49Q22 | Optimal transportation |
| 28C15 | Set functions and measures on topological spaces (regularity of measures, etc.) |
Keywords:
Kantorovich problem; conditional measure; nonlinear cost functional; cost function; Radon marginal distributionsReferences:
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