Constrained Optimal Transport

Ibrahim Ekren, H. Mete Soner

Research output: Contribution to journalArticle

4 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)929-965
Number of pages37
JournalArchive for Rational Mechanics and Analysis
Volume227
Issue number3
DOIs
StatePublished - Mar 1 2018

All Science Journal Classification (ASJC) codes

  • Analysis
  • Mathematics (miscellaneous)
  • Mechanical Engineering

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