@article{15f001ff49074657ac4521dfc56ec6b0,
title = "A Continuation Multiple Shooting Method for Wasserstein Geodesic Equation",
abstract = "In this paper, we propose a numerical method to solve the classic L2-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.",
keywords = "boundary value problem, Hamiltonian flow, multiple shooting method, optimal transport",
author = "Jianbo Cui and Luca Dieci and Haomin Zhou",
note = "Funding Information: \ast Submitted to the journal's Methods and Algorithms for Scientific Computing section May 21, 2021; accepted for publication (in revised form) April 18, 2022; published electronically September 12, 2022. https://doi.org/10.1137/21M142160X Funding: This research was partially supported by the Georgia Tech Mathematics Application Portal (GT-MAP) and by research grants NSF DMS-1620345, NSF DMS-1830225, and ONR N00014-18-1-2852. The research of the first author was partially supported by the Hong Kong Research Grant Council ECS grant 25302822, internal funds P0039016 and P0041274 from The Hong Kong Polytechnic University, and the CAS AMSS-PolyU Joint Laboratory of Applied Mathematics. Publisher Copyright: {\textcopyright} 2022 Society for Industrial and Applied Mathematics Publications. All rights reserved.",
year = "2022",
month = oct,
doi = "10.1137/21M142160X",
language = "English",
volume = "44",
pages = "A2918--A2943",
journal = "SIAM Journal on Scientific Computing",
issn = "1064-8275",
publisher = "Society for Industrial and Applied Mathematics Publications",
number = "5",
}