Abstract: We first give a brief introduction to discrete optimal transport, which can be dated back to Kantorovich's pioneer work in 1940s, for relaxing the original mass transport problem proposed by Monge in 1780s.Then we move to the numerical computation aspect, which adopts the alternating direction method of multipliers (ADMM). By exploring the special structure of the problem itself, we find closed solution form for the subproblem of ADMM, and prove the global linear convergence rate.

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