Solving Large-Scale Optimization Problems with a Convergence Rate Independent of Grid Size
Optimization and Control
2018-05-25 v1 Numerical Analysis
Abstract
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.
Cite
@article{arxiv.1805.09453,
title = {Solving Large-Scale Optimization Problems with a Convergence Rate Independent of Grid Size},
author = {Matt Jacobs and Flavien Léger and Wuchen Li and Stanley Osher},
journal= {arXiv preprint arXiv:1805.09453},
year = {2018}
}