Convergence revisit on generalized symmetric ADMM. (2nd January 2021)

• Record Type: Journal Article
• Authors: Bai, Jianchao; Chang, Xiaokai; Li, Jicheng; Xu, Fengmin
• Is Part Of: Optimization. Volume 70:Number 1(2021)
• Page Start: 149
• Page End: 168
• Publication Date: 2021-01-02
• Subjects: Convex optimization -- alternating direction method of multipliers -- symmetric parameter domain -- convergence rate; 65K10 -- 68W40 -- 90C25; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2019.1704754
• Languages: English
• ISSNs: 0233-1934

Abstract

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.