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A CONTINUATION MULTIPLE SHOOTING METHOD FOR WASSERSTEIN GEODESIC EQUATION
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DOI：10.1137/21M142160X.png)
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摘要
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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.
Keyword:
Hamiltonian flow
boundary value problem
optimal transport
multiple shooting method
期刊
IF:
2.6
论文数:
5.1K
被引数:
1.8W
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