On the pointwise iteration-complexity of a dynamic regularized ADMM with over-relaxation stepsize

TL;DR

This paper extends the pointwise iteration-complexity analysis of a dynamic regularized ADMM to a broader stepsize domain, including over-relaxation, by interpreting it within a hybrid proximal extragradient framework.

Contribution

It broadens the stepsize domain for the complexity analysis of ADMM, allowing stepsizes in (0,2), and provides a new interpretation via a hybrid proximal extragradient framework.

Findings

Allowed stepsize in (0,2) for ADMM complexity analysis

Unified analysis framework using hybrid proximal extragradient method

Enhanced understanding of ADMM iteration complexity

Abstract

In this paper, we extend the improved pointwise iteration-complexity result of a dynamic regularized alternating direction method of multipliers (ADMM) for a new stepsize domain. In this complexity analysis, the stepsize parameter can even be chosen in the interval $(0,2)$ instead of interval $(0,(1+\sqrt{5})/2)$. As usual, our analysis is established by interpreting this ADMM variant as an instance of a hybrid proximal extragradient framework applied to a specific monotone inclusion problem.