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

In this paper, we extend the improved pointwise iteration-complexity estimation of a dynamic regularized alternating direction method of multipliers (ADMM) for a new stepsize domain. In this complexity analysis, the stepsize parameter can be chosen in the interval (0,2) instead of interval (0,(1+5)/2). We illustrate, by means of a numerical experiment, that the enlargement of this stepsize domain can lead to better performance of the method in some applications. Our complexity study is established by interpreting this ADMM variant as an instance of a hybrid proximal extragradient framework applied to a specific monotone inclusion problem.