Abstract
In this note, we show a sublinear nonergodic convergence rate for the algorithm developed in Bai et al. [Generalized symmetric ADMM for separable convex optimization. Comput Optim Appl. 2018;70:129–170], as well as its linear convergence under assumptions that the sub-differential of each component objective function is piecewise linear and all the constraint sets are polyhedra. These remaining convergence results are established for the stepsize parameters of dual variables belonging to a special isosceles triangle region, which aims to strengthen our understanding for convergence of the generalized symmetric ADMM.
Acknowledgments
The authors wish to thank the Editor-in-Chief Prof. Christiane Tammer and the anonymous referees for providing their valuable suggestions, which have significantly improved the quality of our paper.
Disclosure statement
No potential conflict of interest was reported by the authors.