On the iteration-complexity of a non-Euclidean hybrid proximal extragradient framework and of a proximal ADMM

Abstract

ABSTRACTPointwise and ergodic iteration-complexity results for the proximal alternating direction method of multipliers (ADMM) for any stepsize in have been recently established in the literature. In addition to giving alternative proofs of these results, this paper also extends the ergodic iteration-complexity result to include the case in which the stepsize is equal to . As far as we know, this is the first ergodic iteration-complexity for the stepsize obtained in the ADMM literature. These results are obtained by showing that the proximal ADMM is an instance of a non-Euclidean hybrid proximal extragradient framework whose pointwise and ergodic convergence rate are also studied.