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Extending the ergodic convergence rate of the proximal ADMM

Max Leandro Nobre Gonçalves(maxlngoncalves***at***gmail.com)
Jefferson Gonçalves Melo(jefferson.ufg***at***gmail.com)
Renato D.C. Monteiro(rm88***at***gatech.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: 11/09/2016
Entry Accepted: 11/09/2016
Entry Last Modified: 11/09/2016

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