Proximal Iterative Hard Thresholding Algorithm for Sparse Group ℓ₀-Regularized Optimization with Box Constraint

2025/05/30 by Yangyi Ye, Qingna Li, Ye, Yuge +1
Engineering · Mathematics · #FOS: Mathematics #Numerical methods in inverse problems #Optimization and Control (math.OC) #Photoacoustic and Ultrasonic Imaging #Sparse and Compressive Sensing Techniques

paper · pdf · doi:10.48550/arxiv.2506.00196

openalex publication_date 2025/05/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper investigates a general class of problems in which a lower bounded smooth convex function incorporating ℓ₀ and ℓ_2,0 regularization is minimized over a box constraint. Although such problems arise frequently in practical applications, their inherent non-convexity poses significant challenges for solution methods. In particular, we focus on the proximal operator associated with these regularizations, which incorporates both group-sparsity and element-wise sparsity terms. Besides, we introduce the concepts of τ-stationary point and support optimal (SO) point then analyze their relationship with the minimizer of the considered problem. Based on the proximal operator, we propose a novel proximal iterative hard thresholding algorithm to solve the problem. Furthermore, we establish the global convergence and the computational complexity analysis of the proposed method. Finally, extensive experiments demonstrate the effectiveness and efficiency of our method.

Citations

• A Survey of Recent Advances in Optimization Methods for Wireless Communications
• Proximal alternating linearized minimization for nonconvex and nonsmooth problems
• A Sparse-Group Lasso
• Sparse group lasso and high dimensional multinomial classification
• A Selective Review of Group Selection in High-Dimensional Models
• Collaborative Hierarchical Sparse Modeling
• A note on the group lasso and a sparse group lasso
• Decoding by Linear Programming
• Finite-dimensional variational inequality and nonlinear complementarity problems: A survey of theory, algorithms and applications

Related

• An accelerated proximal iterative hard thresholding method for ℓ₀ minimization
• Group sparse optimization via ℓ_p,q regularization
• Sparsity via Sparse Group k-max Regularization
• An Efficient and Globally Convergent Algorithm for ℓ_p,q-ℓ_r Model in Group Sparse Optimization
• Subspace Newton's Method for ℓ₀-Regularized Optimization Problems with Box Constraint