Dynamic Optimal Transport with Optimal Star‐Shaped Graphs

Marcello Carioni; Juliane Krautz; Jan‐Frederik Pietschmann

doi:10.1002/pamm.70076

Dynamic Optimal Transport with Optimal Star‐Shaped Graphs

Marcello Carioni
, Juliane Krautz
, Jan‐Frederik Pietschmann

Mathematics of Imaging & AI

Research output: Contribution to journal › Article › Academic › peer-review

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Abstract

We study an optimal transport problem in a compact convex set
where bulk transport is coupled to dynamic optimal transport on a metric graph
which is embedded in . We prove the existence of solutions for fixed graphs. Next, we consider varying graphs, yet only for the case of star-shaped ones. Here, the action functional is augmented by an additional penalty that prevents the edges of the graph from overlapping. This allow us to preserve the graph topology and thus to rely on standard techniques in calculus of variations in order to show the existence of minimizers.

Original language	English
Article number	e70076
Number of pages	7
Journal	Proceedings in Applied Mathematics and Mechanics
Volume	26
Issue number	1
Early online date	18 Jan 2026
DOIs	https://doi.org/10.1002/pamm.70076
Publication status	Published - Mar 2026
Event	95th Annual Meeting of the International Association of Applied Mathematics and Mechanics, GAMM 2025: Memories from Poznan - Poznan University of Technology, Poznan, Poland Duration: 7 Apr 2025 → 11 Apr 2025 Conference number: 95 https://jahrestagung.gamm.org/annual-meeting-2025/95th-annual-meeting-2/

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Dynamic Optimal Transport with optimal star shaped graphs
Carioni, M., Krautz, J. & Pietschmann, J.-F., 17 Jun 2025, ArXiv.org.
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Dynamic Optimal Transport with Optimal Star‐Shaped Graphs

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Dynamic Optimal Transport with optimal star shaped graphs

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