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On the Well‐Posedness of Branched Transportation
Author(s) -
Colombo Maria,
De Rosa Antonio,
Marchese Andrea
Publication year - 2021
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.21919
Subject(s) - generality , limit (mathematics) , stability (learning theory) , mathematics , mathematical optimization , computer science , mathematical analysis , psychotherapist , psychology , machine learning
We show in full generality the stability of optimal transport paths in branched transport: namely, we prove that any limit of optimal transport paths is optimal as well. This solves an open problem in the field (cf. Open problem 1 in the book Optimal transportation networks by Bernot, Caselles, and Morel), which has been addressed up to now only under restrictive assumptions. © 2020 Wiley Periodicals LLC