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arXiv · 1610.02940

Constrained Optimal Transport

Ibrahim Ekren·H. Mete Soner
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Abstract

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.

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Ibrahim Ekren, H. Mete Soner. 2017-09-11. Constrained Optimal Transport. https://doi.org/10.1007/s00205-017-1178-0

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