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.
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Benamou, J.D., Brenier, Y. Mixed L 2-Wasserstein Optimal Mapping Between Prescribed Density Functions. Journal of Optimization Theory and Applications 111, 255–271 (2001). https://doi.org/10.1023/A:1011926116573
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DOI: https://doi.org/10.1023/A:1011926116573