Artstein-Avidan, S., Sadovsky, S. and Wyczesany, K. orcid.org/0000-0002-1530-7916 (2022) A Rockafellar-type theorem for non-traditional costs. Advances in Mathematics, 395. 108157. ISSN 0001-8708
Abstract
In this note, we present a unified approach to the problem of existence of a potential for the optimal transport problem with respect to non-traditional cost functions, that is costs that assume infinite values. We establish a new method which relies on proving solvability of a special (possibly infinite) family of linear inequalities. We give a necessary and sufficient condition on the coefficients that assure the existence of a solution, and which in the setting of transport theory we call c-path-boundedness. This condition fully characterizes sets that admit a potential and replaces c-cyclic monotonicity from the classical theory, i.e. when the cost is real-valued. Our method also gives a new and elementary proof for the classical results of Rockafellar, Rochet and Rüschendorf.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2021 Elsevier. This is an author produced version of an article accepted for publication in Advances in Mathematics. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Optimal transport; Existence of a potential; c-path-boundedness; c-cyclic monotonicity; Rockafellar-type theorem |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 16 Jan 2025 16:12 |
Last Modified: | 17 Jan 2025 08:00 |
Status: | Published |
Publisher: | Elsevier |
Identification Number: | 10.1016/j.aim.2021.108157 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:221835 |