2024/12/21 by Hong Zhu, Zhu, Hong · 1 citation
Computer Science · Engineering · Mathematics · #90C26 49M15 65K05 #Advanced Optimization Algorithms Research #FOS: Mathematics #Optimization and Control (math.OC) #Optimization and Variational Analysis #Topology Optimization in Engineering
paper · pdf · doi:10.48550/arxiv.2412.16535
openalex publication_date 2024/12/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we propose an inexact proximal Newton-type method for nonconvex composite problems. We establish the global convergence rate of the order O(k-1/2) in terms of the minimal norm of the KKT residual mapping and the local superlinear convergence rate in terms of the sequence generated by the proposed algorithm under the higher-order metric q-subregularity property. When the Lipschitz constant of the corresponding gradient is known, we show that the proposed algorithm is well-defined without line search. Extensive numerical experiments on the ℓ1-regularized Student's t-regression and the group penalized Student's t-regression show that the performance of the proposed method is comparable to the state-of-the-art proximal Newton-type methods.