- Convergence Study on the Proximal Alternating Direction Method with Larger Step Size Bingsheng He(hebmanju.edu.cn) Feng Ma(mafengnjugmail.com) Abstract: The alternating direction method of multipliers (ADMM) is a popular method for the separable convex programming with linear constraints, and the proximal ADMM is its important variant. Previous studies show that the relaxation factor $\gamma\in (0, \frac{1+\sqrt{5}}{2})$ by Fortin and Glowinski for the ADMM is also valid for the proximal ADMM. In this paper, we further demonstrate that the feasible region of $\gamma$ depends on the proximal term added on the second subproblem, and can be enlarged when the proximal factor is positive. We derive the exact relationship between the relaxation factor $\gamma$ and the proximal factor. Finally, we prove the global convergence and derive a worst-case $O(1/t)$ convergence rate in the ergodic sense for this generalized scheme. Keywords: Alternating Direction Method of Multipliers, Convex Programming, Proximal Regularization, Contraction, Convergence Analysis. Category 1: Convex and Nonsmooth Optimization Citation: Download: [PDF]Entry Submitted: 02/12/2017Entry Accepted: 02/12/2017Entry Last Modified: 02/12/2017Modify/Update this entry Visitors Authors More about us Links Subscribe, Unsubscribe Digest Archive Search, Browse the Repository Submit Update Policies Coordinator's Board Classification Scheme Credits Give us feedback Optimization Journals, Sites, Societies Optimization Online is supported by the Mathematical Optmization Society.