Journal
SIAM JOURNAL ON SCIENTIFIC COMPUTING
Volume 44, Issue 5, Pages A2918-A2943Publisher
SIAM PUBLICATIONS
DOI: 10.1137/21M142160X
Keywords
Hamiltonian flow; boundary value problem; optimal transport; multiple shooting method
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Funding
- Georgia Tech Mathematics Application Portal (GT-MAP)
- NSF [DMS-1620345, DMS-1830225]
- ONR [N00014-18-1-2852]
- Hong Kong Research Grant Council ECS [25302822]
- Hong Kong Polytechnic University [P0039016, P0041274]
- CAS AMSS-PolyU Joint Laboratory of Applied Mathematics
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This paper proposes a numerical method for solving the classic L-2-optimal transport problem. The algorithm is based on multiple shooting and a continuation procedure to solve the associated boundary value problem. By considering the viewpoint of Wasserstein Hamiltonian flow, the algorithm reflects the Hamiltonian structure of the problem and utilizes it in the numerical discretization. Several numerical examples are provided to demonstrate the performance of the method.
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.
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