A dual active-set proximal Newton algorithm for sparse approximation of correlation matrices. (3rd September 2022)

• Record Type: Journal Article
• Authors: Liu, Xiao; Shen, Chungen; Wang, Li
• Is Part Of: Optimization methods and software. Volume 37:Number 5(2022)
• Page Start: 1820
• Page End: 1844
• Publication Date: 2022-09-03
• Subjects: Sparse approximation -- correlation matrices -- proximal gradient method -- semi-smooth Newton method -- global convergence; 90C30; Mathematical optimization -- Periodicals; Algorithms -- Periodicals; 519.7
• DOI: 10.1080/10556788.2021.1998491
• Languages: English
• ISSNs: 1055-6788

Abstract

Abstract : In this paper, we propose a novel dual active-set algorithm that is based on proximal gradient and semi-smooth Newton iterations for the sparse approximation of correlation matrices in the Frobenius norm. A new dual formulation with upper and lower bounds is derived. To solve the dual, the proximal gradient method is developed to guarantee global convergence. Also, it provides information to estimate active/inactive constraints. Then, the semi-smooth Newton method is applied to accelerate the convergence of the proximal gradient method, which is the key ingredient of our algorithm. It is shown that the proposed algorithm for the dual is globally convergent under certain conditions. Some preliminary numerical results are given to illustrate the effectiveness of our algorithm on synthetic and real data sets.