Dynamic characterization of barycentric optimal transport problems and their martingale relaxation
Abstract
We extend the Benamou-Brenier formula from classical optimal transport to weak optimal transport and show that the barycentric optimal transport problem studied by Gozlan and Juillet has a dynamic analogue. We also investigate a martingale relaxation of this problem, and relate it to the martingale Benamou-Brenier formula of Backhoff-Veraguas, Beiglböck, Huesmann and Källblad.
Fields of Study & Subjects
Geometric Analysis and Curvature Flows
Navier-Stokes equation solutions
Optimization and Variational Analysis
Publication details
- Journal / source
- Electronic Communications in Probability
- Volume
- 31
- Issue
- none
- Publication date
- 1 January 2026