A Continuation Multiple Shooting Method for Wasserstein Geodesic Equation

Jianbo Cui, Luca Dieci, Haomin Zhou

Abstract: In this paper, we propose a numerical method to solve the classic $L^2$-optimal transport problem. Our algorithm is based on the use of multiple shooting, in combination with a continuation procedure, to solve the boundary value problem associated to the transport problem. Based on the viewpoint of Wasserstein Hamiltonian flow with initial and target densities, our algorithm reflects the Hamiltonian structure of the underlying problem and exploits it in the numerical discretization. Several numerical examples are presented to illustrate the performance of the method.