Unbalanced and Partial $$L_1$$L1 Monge–Kantorovich Problem: A Scalable Parallel First-Order Method

We propose a new algorithm to solve the unbalanced and partial $$L_1$$L1-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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