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On the extremal points of the ball of the Benamou–Brenier energy

Bredies, Kristian; Carioni, Marcello; Fanzon, Silvio; Romero, Francisco

Authors

Kristian Bredies

Marcello Carioni

Francisco Romero



Abstract

In this paper, we characterize the extremal points of the unit ball of the Benamou–Brenier energy and of a coercive generalization of it, both subjected to the homogeneous continuity equation constraint. We prove that extremal points consist of pairs of measures concentrated on absolutely continuous curves which are characteristics of the continuity equation. Then, we apply this result to provide a representation formula for sparse solutions of dynamic inverse problems with finite-dimensional data and optimal-transport based regularization.

Citation

Bredies, K., Carioni, M., Fanzon, S., & Romero, F. (2021). On the extremal points of the ball of the Benamou–Brenier energy. Bulletin of the London Mathematical Society, 53(5), 1436-1452. https://doi.org/10.1112/blms.12509

Journal Article Type Article
Acceptance Date May 1, 2021
Online Publication Date Jun 26, 2021
Publication Date Oct 1, 2021
Deposit Date May 9, 2023
Publicly Available Date May 12, 2023
Journal Bulletin of the London Mathematical Society
Print ISSN 0024-6093
Electronic ISSN 1469-2120
Publisher Wiley
Peer Reviewed Peer Reviewed
Volume 53
Issue 5
Pages 1436-1452
DOI https://doi.org/10.1112/blms.12509
Public URL https://hull-repository.worktribe.com/output/4271004

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Copyright Statement
© 2021 The Authors. Bulletin of the London Mathematical Society is copyright © London Mathematical Society. This is an open access article under the terms of the Creative Commons Attribution License, which
permits use, distribution and reproduction in any medium, provided the original work is properly cited.




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