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|Abstract:||© 2017, Springer-Verlag GmbH Germany. The classical duality theory of Kantorovich (C R (Doklady) Acad Sci URSS (NS) 37:199–201, 1942) and Kellerer (Z Wahrsch Verw Gebiete 67(4):399–432, 1984) for 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 X with an order unit. The problem is given as the supremum over a convex subset of the positive unit sphere of the topological dual of X and the dual problem is defined on the bi-dual of X. These results are then applied to several extensions of the classical optimal transport.|
|Citation:||Ekren, I, Soner, HM. (2018). Constrained Optimal Transport. Archive for Rational Mechanics and Analysis, 227 (3), 929 - 965. doi:10.1007/s00205-017-1178-0|
|Pages:||929 - 965|
|Type of Material:||Journal Article|
|Journal/Proceeding Title:||Archive for Rational Mechanics and Analysis|
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