Robust Convergence Analysis of Three-Operator Splitting
Abstract
Operator splitting methods solve composite optimization problems by breaking them into smaller sub-problems that can be solved sequentially or in parallel. In this paper, we propose a unified framework for certifying both linear and sublinear convergence rates for three-operator splitting (TOS) method under a variety of assumptions about the objective function. By viewing the algorithm as a dynamical system with feedback uncertainty (the oracle model), we leverage robust control theory to analyze the worst-case performance of the algorithm using matrix inequalities. We then show how these matrix inequalities can be used to verify sublinear/linear convergence of the TOS algorithm and guide the search for selecting the parameters of the algorithm (both symbolically and numerically) for optimal worst-case performance. We illustrate our results numerically by solving an input-constrained optimal control problem.
Cite
@article{arxiv.1910.04229,
title = {Robust Convergence Analysis of Three-Operator Splitting},
author = {Han Wang and Mahyar Fazlyab and Shaoru Chen and Victor M. Preciado},
journal= {arXiv preprint arXiv:1910.04229},
year = {2019}
}