2012/09/29 by Zhaosong Lu, Lu, Zhaosong · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Optimization Algorithms Research #Computation (stat.CO) #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Optimization and Control (math.OC) #Optimization and Variational Analysis #Sparse and Compressive Sensing Techniques
paper · pdf · doi:10.48550/arxiv.1210.0066
openalex publication_date 2012/09/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we study general lp regularized unconstrained minimization problems. In particular, we derive lower bounds for nonzero entries of first- and second-order stationary points, and hence also of local minimizers of the lp minimization problems. We extend some existing iterative reweighted l1 (IRL1) and l2 (IRL2) minimization methods to solve these problems and proposed new variants for them in which each subproblem has a closed form solution. Also, we provide a unified convergence analysis for these methods. In addition, we propose a novel Lipschitz continuous ε-approximation to ‖x‖pp. Using this result, we develop new IRL1 methods for the lp minimization problems and showed that any accumulation point of the sequence generated by these methods is a first-order stationary point, provided that the approximation parameter ε is below a computable threshold value. This is a remarkable result since all existing iterative reweighted minimization methods require that ε be dynamically updated and approach zero. Our computational results demonstrate that the new IRL1 method is generally more stable than the existing IRL1 methods [21,18] in terms of objective function value and CPU time.