A CONTINUATION MULTIPLE SHOOTING METHOD FOR WASSERSTEIN GEODESIC EQUATION

被引：4

作者：

Cui, Jianbo ^{[1
,2
]}

Dieci, Luca

Zhou, Haomin ^{[1
]}

机构：

[1] Georgia Inst Technol, Sch Math, Atlanta, GA 30332 USA

[2] Hong Kong Polytech Univ, Dept Appl Math, Kowloon, Hong Kong, Peoples R China

来源：

SIAM JOURNAL ON SCIENTIFIC COMPUTING | 2022年 / 44卷 / 05期

关键词：

Hamiltonian flow; boundary value problem; optimal transport; multiple shooting method; OPTIMAL TRANSPORT DISTANCE; NUMERICAL-SOLUTION; ALGORITHM; VECTOR;

D O I：

10.1137/21M142160X

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we propose a numerical method to solve the classic L-2-optimal trans-port 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.

引用

页码：A2918 / A2943

页数：26

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