Solving Large-Scale Optimization Problems with a Convergence Rate Independent of Grid Size
Provides a practical solution for large-scale image denoising and optimal transport problems that previously suffered from grid-size-dependent convergence.
The paper presents a primal-dual method for solving L1-type non-smooth optimization problems with convergence rate independent of grid size, enabling solution of 4096x4096 problems in minutes without parallelization.
We present a primal-dual method to solve L1-type non-smooth optimization problems independently of the grid size. We apply these results to two important problems : the Rudin-Osher-Fatemi image denoising model and the L1 earth mover's distance from optimal transport. Crucially, we provide analysis that determines the choice of optimal step sizes and we prove that our method converges independently of the grid size. Our approach allows us to solve these problems on grids as large as 4096 by 4096 in a few minutes without parallelization.