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Mathematical Problems in Engineering
Volume 2017, Article ID 9674528, 15 pages
Research Article

A Proximal Fully Parallel Splitting Method for Stable Principal Component Pursuit

1School of Mathematics and Statistics, Linyi University, Shandong 276005, China
2School of Data Sciences, Zhejiang University of Finance and Economics, Zhejiang 310018, China
3School of Mathematics and Statistics, Zaozhuang University, Shandong 277160, China
4School of Management, Qufu Normal University, Shandong 276826, China

Correspondence should be addressed to Min Sun; moc.361@uodoaixuoyiz

Received 30 March 2017; Revised 8 June 2017; Accepted 29 August 2017; Published 25 October 2017

Academic Editor: Laurent Bako

Copyright © 2017 Hongchun Sun et al. 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.


As a special three-block separable convex programming, the stable principal component pursuit (SPCP) arises in many different disciplines, such as statistical learning, signal processing, and web data ranking. In this paper, we propose a proximal fully parallel splitting method (PFPSM) for solving SPCP, in which the resulting subproblems all admit closed-form solutions and can be solved in distributed manners. Compared with other similar algorithms in the literature, PFPSM attaches a Glowinski relaxation factor to the updating formula for its Lagrange multiplier, which can be used to accelerate the convergence of the generated sequence. Under mild conditions, the global convergence of PFPSM is proved. Preliminary computational results show that the proposed algorithm works very well in practice.