Geodesic
Existence of Solutions to the Nonlinear Kantorovich Transportation Problem
Matematičeskie zametki, Tome 112 (2022) no. 3, pp. 360-370

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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.
Keywords: Kantorovich problem, conditional measure, nonlinear cost functional, cost function. 
@article{MZM_2022_112_3_a3,
     author = {V. I. Bogachev and A. V. Rezbayev},
     title = {Existence of {Solutions} to the {Nonlinear} {Kantorovich} {Transportation} {Problem}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {360--370},
     publisher = {mathdoc},
     volume = {112},
     number = {3},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2022_112_3_a3/}
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V. I. Bogachev; A. V. Rezbayev. Existence of Solutions to the Nonlinear Kantorovich Transportation Problem. Matematičeskie zametki, Tome 112 (2022) no. 3, pp. 360-370. http://geodesic.mathdoc.fr/item/MZM_2022_112_3_a3/