Year: 2020
Author: Adam M. Oberman, Yuanlong Ruan
Journal of Computational Mathematics, Vol. 38 (2020), Iss. 6 : pp. 933–951
Abstract
We compute and visualize solutions to the Optimal Transportation (OT) problem for a wide class of cost functions. The standard linear programming (LP) discretization of the continuous problem becomes intractable for moderate grid sizes. A grid refinement method results in a linear cost algorithm. Weak convergence of solutions is established and barycentric projection of transference plans is used to improve the accuracy of solutions. Optimal maps between nonconvex domains, partial OT free boundaries, and high accuracy barycenters are presented.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.1907-m2017-0224
Journal of Computational Mathematics, Vol. 38 (2020), Iss. 6 : pp. 933–951
Published online: 2020-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 19
Keywords: Optimal Transportation Linear Programming Monge-Kantorovich Barycenter.