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This work is concerned with the efficient optimization method for solving alarge class of optimal mass transport problems. An inexact primal-dualalgorithm is presented from the time discretization of a proper dynamicalsystem, and by using the tool of Lyapunov function, the global (super-)linearconvergence rate is established for function residual and feasibilityviolation. The proposed algorithm contains an inner problem that possessesstrong semismoothness property and motivates the use of the semismooth Newtoniteration. By exploring the hidden structure of the problem itself, the linearsystem arising from the Newton iteration is transferred equivalently into agraph Laplacian system, for which a robust algebraic multigrid method isproposed and also analyzed via the famous Xu--Zikatanov identity. Finally,numerical experiments are provided to validate the efficiency of our method.

An efficient semismooth Newton-AMG-based inexact primal-dual algorithm for generalized transport problems