2023/12/25 by Yuqia Wu, Wu, Yuqia, Shaohua Pan +3 · 2 citations
Computer Science · Engineering · Mathematics · #FOS: Mathematics #Numerical methods in inverse problems #Optimization and Control (math.OC) #Optimization and Variational Analysis #Sparse and Compressive Sensing Techniques
paper · doi:10.48550/arxiv.2312.15718
openalex publication_date 2023/12/25 · openalex created_date 2023/12/29 · openalex updated_date 2026/07/28
We are concerned with structured ℓ0-norms regularization problems, with a twice continuously differentiable loss function and a box constraint. This class of problems have a wide range of applications in statistics, machine learning and image processing. To the best of our knowledge, there is no effective algorithm in the literature for solving them. In this paper, we first obtain a polynomial-time algorithm to find a point in the proximal mapping of the fused ℓ0-norms with a box constraint based on dynamic programming principle. We then propose a hybrid algorithm of proximal gradient method and inexact projected regularized Newton method to solve structured ℓ0-norms regularization problems. The whole sequence generated by the algorithm is shown to be convergent by virtue of a non-degeneracy condition, a curvature condition and a Kurdyka-Łojasiewicz property. A superlinear convergence rate of the iterates is established under a locally Hölderian error bound condition on a second-order stationary point set, without requiring the local optimality of the limit point. Finally, numerical experiments are conducted to highlight the features of our considered model, and the superiority of our proposed algorithm.