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Convex duality in nonlinear optimal transport

Research output: Contribution to journalArticle

Teemu August Pennanen, Ari-Pekka Perkkio

Original languageEnglish
Pages (from-to)1029-1060
Number of pages32
JournalJOURNAL OF FUNCTIONAL ANALYSIS
Volume277
Issue number4
Early online date16 May 2019
DOIs
Accepted/In press19 Apr 2019
E-pub ahead of print16 May 2019
Published15 Aug 2019

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Abstract

This article studies problems of optimal transport, by embedding them in a general functional analytic framework of convex optimization. This provides a unified treatment of a large class of related problems in probability theory and allows for generalizations of the classical problem formulations. General results on convex duality yield dual problems and optimality conditions for these problems. When the objective takes the form of a convex integral functional, we obtain more explicit optimality conditions and establish the existence of solutions for a relaxed formulation of the problem. This covers, in particular, the mass transportation problem and its nonlinear generalizations.

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