Extending the ergodic convergence rate of the proximal ADMM
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})/$. 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
Cite
@article{arxiv.1611.02903,
title = {Extending the ergodic convergence rate of the proximal ADMM},
author = {Max L. N. Goncalves and Jefferson G. Melo and Renato D. C. Monteiro},
journal= {arXiv preprint arXiv:1611.02903},
year = {2016}
}
Comments
arXiv admin note: text overlap with arXiv:1601.01140