A trust region-type normal map-based semismooth Newton method for nonsmooth nonconvex composite optimization

• 成果类型: Article
• 署名作者: Ouyang, Wenqing; Milzarek, Andre
• 署名单位: Shenzhen Research Institute of Big Data; Shenzhen Institute of Artificial Intelligence & Robotics for Society; The Chinese University of Hong Kong, Shenzhen
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-024-02110-2
• 发表日期: 2025
• 页码: 389-435
• 关键词: Augmented Lagrangian method; proximal point algorithm; GLOBAL CONVERGENCE; thresholding algorithm; descent methods; minimization; shrinkage; EQUATIONS; compression; selection

摘要

We propose a novel trust region method for solving a class of nonsmooth, nonconvex composite-type optimization problems. The approach embeds inexact semismooth Newton steps for finding zeros of a normal map-based stationarity measure for the problem in a trust region framework. Based on a new merit function and acceptance mechanism, global convergence and transition to fast local q-superlinear convergence are established under standard conditions. In addition, we verify that the proposed trust region globalization is compatible with the Kurdyka-& Lstrok;ojasiewicz inequality yielding finer convergence results. Experiments on sparse logistic regression, image compression, and a constrained log-determinant problem illustrate the efficiency of the proposed algorithm.