Existence of Solutions to the Nonlinear Kantorovich Transportation Problem

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.