A new linear convergence result for the iterative soft thresholding algorithm. (3rd July 2017)

• Record Type: Journal Article
• Authors: Zhang, Lufang; Hu, Yaohua; Li, Chong; Yao, Jen-Chih
• Is Part Of: Optimization. Volume 66:Number 7(2017)
• Page Start: 1177
• Page End: 1189
• Publication Date: 2017-07-03
• Subjects: Iterative soft thresholding algorithm -- linear convergence analysis -- linear inverse problems -- sparsity pattern; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2017.1318133
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : The iterative soft thresholding algorithm (ISTA) is one of the most popular optimization algorithms for solving the regularized least squares problem, and its linear convergence has been investigated under the assumption of finite basis injectivity property or strict sparsity pattern. In this paper, we consider the regularized least squares problem in finite- or infinite-dimensional Hilbert space, introduce a weaker notion of orthogonal sparsity pattern (OSP) and establish the Q-linear convergence of ISTA under the assumption of OSP. Examples are provided to illustrate the cases where the linear convergence of ISTA can be established only by our result, but cannot be ensured by any existing result in the literature.