Geodesic
The nonlinear Kantorovich transportation problem with nonconvex costs
Funkcionalʹnyj analiz i ego priloženiâ, Tome 57 (2023) no. 4, pp. 3-16

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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.
Keywords: Kantorovich problem, conditional measure, nonlinear cost functional, cost function. 
@article{FAA_2023_57_4_a0,
     author = {K. A. Afonin},
     title = {The nonlinear {Kantorovich} transportation problem with nonconvex costs},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {3--16},
     publisher = {mathdoc},
     volume = {57},
     number = {4},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2023_57_4_a0/}
}
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K. A. Afonin. The nonlinear Kantorovich transportation problem with nonconvex costs. Funkcionalʹnyj analiz i ego priloženiâ, Tome 57 (2023) no. 4, pp. 3-16. http://geodesic.mathdoc.fr/item/FAA_2023_57_4_a0/