Constrained Optimal Transport

Understand

The classical duality theory of Kantorovich and Kellerer for the classical optimal transport is generalized to an abstract framework and a characterization of the dual elements is provided.

• This abstract generalization is set in a Banach lattice $\cal{X}$ with a order unit.
• The primal problem is given as the supremum over a convex subset of the positive unit sphere of the topological dual of $\cal{X}$ and the dual problem is defined on the bi-dual of $\cal{X}$.
• These results are then applied to several extensions of the classical optimal transport.