A Proximal Fully Parallel Splitting Method for Stable Principal Component Pursuit

Abstract

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 ∈ ( √ 3/2, 2/ √ 3) 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.

A novel noise-tolerant Zhang neural network for time-varying Lyapunov equation

“…However, noise is ubiquitous in real life, which cannot be ignored completely. For example, in the background extraction from surveillance video with missing and noisy data [16,17], the observed data are often contaminated with additive Gaussian noise. The ZNN with anti-noise property has drawn increasing attention from researchers in recent years.…”