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Unbalanced and Partial \(L_1\) Monge–Kantorovich Problem: A Scalable Parallel First-Order Method

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Abstract

We propose a new algorithm to solve the unbalanced and partial \(L_1\)-Monge–Kantorovich problems. The proposed method is a first-order primal-dual method that is scalable and parallel. The method’s iterations are conceptually simple, computationally cheap, and easy to parallelize. We provide several numerical examples solved on a CUDA GPU, which demonstrate the method’s practical effectiveness.

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Acknowledgements

We would like to thank Professor Wilfrid Gangbo for many fruitful and inspirational discussions on the related topics. The Titan Xp used for this research was donated by the NVIDIA Corporation.

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Authors and Affiliations

  1. Department of Mathematics, University of California, Los Angeles, CA, USA

    Ernest K. Ryu, Wuchen Li, Penghang Yin & Stanley Osher

Authors
  1. Ernest K. Ryu
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  2. Wuchen Li
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  3. Penghang Yin
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  4. Stanley Osher
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Corresponding author

Correspondence to Wuchen Li.

Additional information

This work is partially supported by ONR Grants N000141410683, N000141210838 and DOE Grant DE-SC00183838.

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Ryu, E.K., Li, W., Yin, P. et al. Unbalanced and Partial \(L_1\) Monge–Kantorovich Problem: A Scalable Parallel First-Order Method. J Sci Comput 75, 1596–1613 (2018). https://doi.org/10.1007/s10915-017-0600-y

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