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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 912846, 6 pages
http://dx.doi.org/10.1155/2013/912846
Research Article

Convergence Analysis of the Relaxed Proximal Point Algorithm

1School of Economics and Management, Southeast University, Nanjing 210096, China
2Department of Mathematics, Nanjing University, Nanjing 210093, China

Received 3 May 2013; Accepted 9 June 2013

Academic Editor: Abdellah Bnouhachem

Copyright © 2013 Min Li and Yanfei You. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Recently, a worst-case convergence rate was established for the Douglas-Rachford alternating direction method of multipliers (ADMM) in an ergodic sense. The relaxed proximal point algorithm (PPA) is a generalization of the original PPA which includes the Douglas-Rachford ADMM as a special case. In this paper, we provide a simple proof for the same convergence rate of the relaxed PPA in both ergodic and nonergodic senses.