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This is a Quantitative Study study.

October 20, 2025Open Access

Dynamic Optimal Transport with optimal star shaped graphs

Key Points

Existence of solutions is proven for fixed graphs in an optimal transport problem involving star-shaped graphs.
The study incorporates a penalty to maintain graph topology, enhancing the mathematical approach in this context.
Dynamic optimal transport is coupled with bulk transport within a compact convex set for effective analysis.
Standard techniques from Calculus of Variations are utilized to establish the existence of minimizers.

Abstract

We study an optimal transport problem in a compact convex set Ωᵈ where bulk transport is coupled to dynamic optimal transport on a metric graph G = (V, E) which is embedded in Ω. We prove 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 to overlap. This allows to preserve the graph topology and thus to rely on standard techniques in Calculus of Variations in order to show existence of minimizers.

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Cite This Study

Carioni et al. (Tue,) studied this question.

synapsesocial.com/papers/68f6379bb481a140a36cf65d https://doi.org/https://doi.org/10.48550/arxiv.2506.15007