A Reduced Half Thresholding Algorithm

In this paper, a reduced half thresholding algorithm and its accelerated version, a reduced fast half thresholding algorithm, are proposed for solving large-scale L 1 / 2 -regularized problems. At each iteration, the large-scale original problem is reduced into a sequence of small-scale subproblems,...

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Bibliographic Details
Published in:Journal of scientific computing Vol. 96; no. 2
Main Authors: Liang, Xiubo, Wang, Guoqiang, Yu, Bo
Format: Journal Article
Language:English
Published: New York Springer US 01.08.2023
Subjects:
Algorithms
Computational Mathematics and Numerical Analysis
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Theoretical
Sparse optimization
Thresholding algorithms
regularization
ISSN:0885-7474, 1573-7691
Online Access:Get full text
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Summary:In this paper, a reduced half thresholding algorithm and its accelerated version, a reduced fast half thresholding algorithm, are proposed for solving large-scale L 1 / 2 -regularized problems. At each iteration, the large-scale original problem is reduced into a sequence of small-scale subproblems, and the subproblems are solved by the (fast) half thresholding algorithm. Global convergence of the reduced half thresholding algorithm is proven, and two techniques: the Newton acceleration technique and the shrinking technique are presented to improve the performance. Compared with the state-of-the-art algorithms, the numerical results show that the presented algorithms are promising. As an example, our algorithms are efficient to recover the signal recovery problem with 19,264,097 samples and signal length 29,890,095
ISSN:0885-7474
1573-7691
DOI:10.1007/s10915-023-02250-1