This paper provides a duality gap convergence analysis for the standard ADMM as well as a linearized version of ADMM. It is shown that under appropriate conditions, both methods achieve linear convergence. However, the standard ADMM achieves a faster accelerated convergence rate than that of the linearized ADMM. A simple numerical example is used to illustrate the difference in convergence behavior.
@article{arxiv.1508.03702,
title = {On the Duality Gap Convergence of ADMM Methods},
author = {Da Tang and Tong Zhang},
journal= {arXiv preprint arXiv:1508.03702},
year = {2015}
}