On the extremal points of the ball of the Benamou–Brenier energy
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Peer-reviewed
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Abstract
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.
Description
Funder: Christian Doppler Research Association; Id: http://dx.doi.org/10.13039/501100006012
Funder: Royal Society; Id: http://dx.doi.org/10.13039/501100000288
Keywords
52A05, 49N45, 49J45, 35F05 (primary)
Journal Title
Bulletin of the London Mathematical Society
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Journal ISSN
0024-6093
1469-2120
1469-2120
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Publisher
Wiley
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Sponsorship
Austrian Science Fund (PIR‐27, P 29192)