A customized proximal point algorithm for stable principal component pursuit with nonnegative constraint

Abstract

The stable principal component pursuit (SPCP) problem represents a large class of mathematical models appearing in sparse optimization-related applications such as image restoration, web data ranking. In this paper, we focus on designing a new primal-dual algorithm for the SPCP problem with nonnegative constraint. Our method is based on the framework of proximal point algorithm. By taking full exploitation to the special structure of the SPCP problem, the method enjoys the advantage of being easily implementable. Global convergence result is established for the proposed method. Preliminary numerical results demonstrate that the method is efficient.