Calculus of Variations and Geometric Measure Theory

G. Buttazzo - G. Carlier - K. Eichinger

Wasserstein interpolation with constraints and application to a parking problem

created by buttazzo on 28 Jul 2022


Submitted Paper

Inserted: 28 jul 2022
Last Updated: 28 jul 2022

Year: 2022


We consider optimal transport problems where the cost for transporting a given probability measure $\mu_0$ to another one $\mu_1$ consists of two parts: the first one measures the transportation from $\mu_0$ to an intermediate (pivot) measure $\mu$ to be determined (and subject to various constraints), and the second one measures the transportation from $\mu$ to $\mu_1$. This leads to Wasserstein interpolation problems under constraints for which we establish various properties of the optimal pivot measures $\mu$. Considering the more general situation where only some part of the mass uses the intermediate stop leads to a mathematical model for the optimal location of a parking region around a city. Numerical simulations, based on entropic regularization, are presented both for the optimal parking regions and for Wasserstein constrained interpolation problems.

Keywords: Optimal transport, Wasserstein distance, measure interpolation, optimal parking regions