Operations Research and Optimization

The classical problem of optimal transportation can be formulated as a linear optimization problem on a convex domain: among all joint measures with fixed marginals find the optimal one, where optimality is measured against a given cost function. Here we consider a variation of this problem by imposing an upper bound constraining the joint measures, namely: among all joint measures with fixed marginals and dominated by a fixed measure, find the optimal one. After computing illustrative examples, we given conditions guaranteeing uniqueness of the optimizer and initiate a study of its properties. Based on a preprint arXived with Jonathan Korman.