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http://arks.princeton.edu/ark:/88435/pr1rg5p| 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. |
| Publication Date: | 1-Mar-2018 |
| 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 |
| DOI: | doi:10.1007/s00205-017-1178-0 |
| ISSN: | 0003-9527 |
| EISSN: | 1432-0673 |
| Pages: | 929 - 965 |
| Type of Material: | Journal Article |
| Journal/Proceeding Title: | Archive for Rational Mechanics and Analysis |
| Version: | Author's manuscript |
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