Mixed L 2-Wasserstein Optimal Mapping Between Prescribed Density Functions

J. D. Benamou and Y. Brenier
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J. D. Benamou: INRIA
Y. Brenier: Université Paris 6

Journal of Optimization Theory and Applications, 2001, vol. 111, issue 2, No 2, 255-271

Abstract: Abstract A time-dependent minimization problem for the computation of a mixed L 2-Wasserstein distance between two prescribed density functions is introduced in the spirit of Ref. 1 for the classical Wasserstein distance. The optimum of the cost function corresponds to an optimal mapping between prescribed initial and final densities. We enforce the final density conditions through a penalization term added to our cost function. A conjugate gradient method is used to solve this relaxed problem. We obtain an algorithm which computes an interpolated L 2-Wasserstein distance between two densities and the corresponding optimal mapping.

Keywords: Monge-Kantorovitch mass transfer problem; Wasserstein distance; least-square distance; optimal control; conjugate gradient algorithm (search for similar items in EconPapers)
Date: 2001
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DOI: 10.1023/A:1011926116573

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