Abstract
We demonstrate an iterative scheme to approximate the optimal transportation problem with a discrete target measure under certain standard conditions on the cost function. Additionally, we give a finite upper bound on the number of iterations necessary for the scheme to terminate, in terms of the error tolerance and number of points in the support of the discrete target measure.
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Acknowledgments
The author would like to thank the anonymous referee for a number of comments, in particular, those leading to a much simpler and shorter proof of the result in Remark 5.2.
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Communicated by N. Trudinger.
The author gratefully acknowledges support from a Pacific Institute for the Mathematical Sciences Postdoctoral Fellowship.
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Kitagawa, J. An iterative scheme for solving the optimal transportation problem. Calc. Var. 51, 243–263 (2014). https://doi.org/10.1007/s00526-013-0673-x
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DOI: https://doi.org/10.1007/s00526-013-0673-x