Multi-marginal Entropy-Transport with repulsive cost

In this paper we study theoretical properties of the entropy-transport functional with repulsive cost functions. We provide sufficient conditions for the existence of a minimizer in a class of metric spaces and prove the \(\Gamma\)-convergence of the entropy-transport functional to a multi-marginal...

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Bibliographic Details
Published in:arXiv.org 2019-07
Main Authors: Gerolin, Augusto, Kausamo, Anna, Rajala, Tapio
Format: Article
Language:English
Subjects:
Entropy
Functionals
Online Access:Get full text
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Summary:In this paper we study theoretical properties of the entropy-transport functional with repulsive cost functions. We provide sufficient conditions for the existence of a minimizer in a class of metric spaces and prove the \(\Gamma\)-convergence of the entropy-transport functional to a multi-marginal optimal transport problem with a repulsive cost. We also prove the entropy-regularized version of the Kantorovich duality.
ISSN:2331-8422