Dynamic Optimal Transport with Optimal Star‐Shaped Graphs
Abstract
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.
Fields of Study & Subjects
Geometric Analysis and Curvature Flows
Optimization and Variational Analysis
Topology Optimization in Engineering
Publication details
- Journal / source
- PAMM
- Volume
- 26
- Issue
- 1
- Publication date
- 18 January 2026
- Language
- EN