Iteration complexity on the generalized Peaceman–Rachford splitting method for separable convex programming. (2nd September 2019)

• Record Type: Journal Article
• Authors: Zhang, Xue-Qing; Peng, Jian-Wen; Yao, Jen-Chih
• Is Part Of: Optimization. Volume 68:Number 9(2019)
• Page Start: 1749
• Page End: 1767
• Publication Date: 2019-09-02
• Subjects: Convex minimization problem -- generalized Peaceman–Rachford splitting method -- iteration complexity -- LASSO problem -- matrix optimization; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2019.1636246
• Languages: English
• ISSNs: 0233-1934

Abstract

ABSTRACT: Recently, a generalized version of Peaceman–Rachford splitting method (GPRSM) for solving a convex minimization model with a general separable structure has been proposed and its global convergence has been proved by Sun and Liu. In this paper, we establish the worst-case O ( 1 / t ) convergence rate for the GPRSM in both the ergodic and a nonergodic senses, then we give some numerical results to demonstrate the convergence rate of the GPRSM.