- Extending the ergodic convergence rate of the proximal ADMM Max Leandro Nobre Gonçalves(maxlngoncalvesgmail.com) Jefferson Gonçalves Melo(jefferson.ufggmail.com) Renato D.C. Monteiro(rm88gatech.edu) Abstract: Pointwise and ergodic iteration-complexity 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 iteration-complexity 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 iteration-complexity 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 non-Euclidean hybrid proximal extragradient framework whose pointwise and ergodic convergence rate are also studied. Keywords: alternating direction method of multipliers, hybrid proximal extragradient method, non-Euclidean Bregman distances, convex program, pointwise iteration-complexity, ergodic iteration-complexity, first-order 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 74001-970, Goiania-GO, Brazil Download: [PDF]Entry Submitted: 11/09/2016Entry Accepted: 11/09/2016Entry Last Modified: 11/09/2016Modify/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.