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Max Leandro Nobre Gonçalves(maxlngoncalvesgmail.com) Abstract: Pointwise and ergodic iterationcomplexity results for the proximal alternating direction method of multipliers (ADMM) for any stepsize in $(0,(1+\sqrt{5})/2)$ have been recently established in the literature. In addition to giving alternative proofs of these results, this paper also extends the ergodic iterationcomplexity result to include the case in which the stepsize is equal to $(1+\sqrt{5})/2$. As far as we know, this is the first ergodic iterationcomplexity for the stepsize $(1+\sqrt{5})/2$ obtained in the ADMM literature. These results are obtained by showing that the proximal ADMM is an instance of a nonEuclidean hybrid proximal extragradient framework whose pointwise and ergodic convergence rate are also studied. Keywords: alternating direction method of multipliers, hybrid proximal extragradient method, nonEuclidean Bregman distances, convex program, pointwise iterationcomplexity, ergodic iterationcomplexity, firstorder methods, inexact proximal point method, regular distance generating function. Category 1: Convex and Nonsmooth Optimization (Convex Optimization ) Category 2: Convex and Nonsmooth Optimization (Nonsmooth Optimization ) Citation: Institute of Mathematics and Statistics, Federal University of Goias, Campus II Caixa Postal 131, CEP 74001970, GoianiaGO, Brazil Download: [PDF] Entry Submitted: 11/09/2016 Modify/Update this entry  
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