A continuation multiple shooting method for Wasserstein geodesic equation

In this paper, we propose a numerical method to solve the classic \(L^2\)-optimal transport problem. Our algorithm is based on use of multiple shooting, in combination with a continuation procedure, to solve the boundary value problem associated to the transport problem. We exploit the viewpoint of...

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Bibliographic Details
Published inarXiv.org
Main Authors Cui, Jianbo, Dieci, Luca, Zhou, Haomin
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 20.05.2021
Subjects
Algorithms
Boundary value problems
Numerical methods
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Summary:In this paper, we propose a numerical method to solve the classic \(L^2\)-optimal transport problem. Our algorithm is based on use of multiple shooting, in combination with a continuation procedure, to solve the boundary value problem associated to the transport problem. We exploit the viewpoint of Wasserstein Hamiltonian flow with initial and target densities, and our method is designed to retain the underlying Hamiltonian structure. Several numerical examples are presented to illustrate the performance of the method.
ISSN:2331-8422