On the iteration-complexity of a non-Euclidean hybrid proximal extragradient framework and of a proximal ADMM. (2nd April 2020)

• Record Type: Journal Article
• Authors: Gonçalves, Max L. N.; Melo, Jefferson G.; Monteiro, Renato D. C.
• Is Part Of: Optimization. Volume 69:Number 4(2020)
• Page Start: 847
• Page End: 873
• Publication Date: 2020-04-02
• Subjects: Alternating direction method of multipliers -- hybrid proximal extragradient method -- non-Euclidean Bregman distances -- iteration-complexity; 90C60 -- 90C30 -- 90C25 -- 49M27; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2019.1652297
• Languages: English
• ISSNs: 0233-1934

Abstract

ABSTRACT: Pointwise and ergodic iteration-complexity results for the proximal alternating direction method of multipliers (ADMM) for any stepsize in ( 0, ( 1 + 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 + 5 ) / 2 . As far as we know, this is the first ergodic iteration-complexity for the stepsize ( 1 + 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.