Scaled Proximal Gradient Methods for Sparse Optimization Problems

Thresholding-based methods are widely used for sparse optimization problems in many applications including compressive sensing, image processing, and machine learning. However, the hard thresholding method may converge slowly or diverge for many practical problems. In this paper, we propose a scaled...

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Bibliographic Details
Published in:Journal of scientific computing 2024, Vol.98 (1), p.2, Article 2
Main Authors: Xiao, Guiyun, Zhang, Shuqin, Bai, Zheng-Jian
Format: Article
Language:English
Subjects:
Algorithms
Computational Mathematics and Numerical Analysis
Convergence
Image processing
Machine learning
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Methods
Optimization
Theoretical
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Summary:Thresholding-based methods are widely used for sparse optimization problems in many applications including compressive sensing, image processing, and machine learning. However, the hard thresholding method may converge slowly or diverge for many practical problems. In this paper, we propose a scaled proximal gradient method for solving sparse optimization problems, where the scaled matrix can take a varying positive diagonal for connecting the residual reduction. The global convergence of the proposed method is established under some mild assumptions without the restricted isometry property condition. We also present a scaled proximal pursuit and a modified scaled proximal gradient method with global convergence under the restricted isometry property. Finally, some numerical tests are reported to illustrate the efficiency of the proposed methods over the classical thresholding-based methods.
ISSN:0885-7474
1573-7691
DOI:10.1007/s10915-023-02393-1