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Iteration complexity on the Generalized Peaceman-Rachford splitting method for separable convex programming

Zhang Xue-Qing (zxqcqspb***at***163.com)
Peng Jian-Wen (jwpeng168***at***hotmail.com)

Abstract: Recently, a generalized version of Peaceman-Rachford splitting method (GPRSM) for solving a convex minmization model with a general separable structure has been proposed by \textbf{Sun} et al and its global convergence has been proved. In this paper, we further study theoretical aspects of the generalized Peaceman-Rachford splitting method. We first establish the worst-case $\mathcal{O}(1/t)$ convergence rate for the proposed GPRSM in both the ergodic and a nonergodic senses, then we give some numerical results to demonstrate the convergence rate of the algorithm.

Keywords: Convex minimization problem; Generalized Peaceman-Rachford splitting method; Iteration complexity; LASSO problem; Matrix optimization.

Category 1: Convex and Nonsmooth Optimization (Convex Optimization )

Citation: July 8, 2017

Download: [PDF]

Entry Submitted: 07/07/2017
Entry Accepted: 07/08/2017
Entry Last Modified: 07/07/2017

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