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We present a primal-dual method to solve L1-type non-smooth optimizationproblems independently of the grid size. We apply these results to twoimportant problems : the Rudin-Osher-Fatemi image denoising model and the L1earth mover's distance from optimal transport. Crucially, we provide analysisthat determines the choice of optimal step sizes and we prove that our methodconverges independently of the grid size. Our approach allows us to solve theseproblems on grids as large as 4096 by 4096 in a few minutes withoutparallelization.

Solving Large-Scale Optimization Problems with a Convergence Rate Independent of Grid Size