A General Analysis of the Convergence of ADMM
Abstract
We provide a new proof of the linear convergence of the alternating direction method of multipliers (ADMM) when one of the objective terms is strongly convex. Our proof is based on a framework for analyzing optimization algorithms introduced in Lessard et al. (2014), reducing algorithm convergence to verifying the stability of a dynamical system. This approach generalizes a number of existing results and obviates any assumptions about specific choices of algorithm parameters. On a numerical example, we demonstrate that minimizing the derived bound on the convergence rate provides a practical approach to selecting algorithm parameters for particular ADMM instances. We complement our upper bound by constructing a nearly-matching lower bound on the worst-case rate of convergence.
Keywords
Cite
@article{arxiv.1502.02009,
title = {A General Analysis of the Convergence of ADMM},
author = {Robert Nishihara and Laurent Lessard and Benjamin Recht and Andrew Packard and Michael I. Jordan},
journal= {arXiv preprint arXiv:1502.02009},
year = {2015}
}
Comments
10 pages, 6 figures