LAUSR

We present a new approach to the problem of existence of a potential for the optimal transport problem with respect to non-traditional cost functions, that is, costs that may assume infinite values. We define a notion of c-path-boundedness, and prove that this property characterizes sets that are contained in the c-subgradient of a c-class function. We provide an example of a c-cyclically monotone set which does not admit a potential, and on the other hand, we present cases where c-path-boundedness is implied by c-cyclic monotonicity. Our method also gives a new proof for the Rockafellar-Ruschendorf theorem.