Dynamic Optimal Transport with optimal star shaped graphs

2025/06/17 by Marcello Carioni, Carioni, Marcello, Juliane Krautz +3
Computer Science · Engineering · Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Optimization and Search Problems #Stochastic processes and statistical mechanics #Vehicle Routing Optimization Methods

paper · pdf · doi:10.48550/arxiv.2506.15007

openalex publication_date 2025/06/17 · openalex created_date 2025/10/19 · openalex updated_date 2026/07/28

Abstract

We study an optimal transport problem in a compact convex set Ω⊂ℝ^d 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.

Citations

• Dynamic Optimal Transport with Optimal Preferential Paths
• Gradient flows on metric graphs with reservoirs: Microscopic derivation and multiscale limits
• Gradient flow formulation of diffusion equations in the Wasserstein space over a metric graph
• Dynamic optimal transport on networks
• A new transportation distance with bulk/interface interactions and flux penalization
• On a class of modified Wasserstein distances induced by concave mobility functions defined on bounded intervals

Related

• Dynamic optimal transport on networks
• Dynamic Optimal Transport with Optimal Preferential Paths
• Vector valued optimal transport: from dynamic to static formulations
• Homogenisation of dynamical optimal transport on periodic graphs
• Optimal Transport on Discrete Domains