Two Typical Implementable Semismooth* Newton Methods for Generalized Equations Are G-Semismooth Newton Methods

• 成果类型: Article
• 署名作者: Chen, Liang; Sun, Defeng; Zhang, Wangyongquan
• 署名单位: Hunan University; Hong Kong Polytechnic University
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X; 1526-5471
• DOI: 10.1287/moor.2024.0617
• 发表日期: 2026-08
• 关键词: semismooth* Newton method; generalized equation; nonsmooth analysis; variational analysis; G-semismooth; Augmented Lagrangian method; local convergence; semidefinite; constraint; THEOREMS

摘要

Semismooth* Newton methods have been proposed in recent years targeting multivalued inclusion problems and have been successfully implemented to deal with several concrete generalized equations. In this paper, we show that two typical implementations of them that are available are exactly the applications of G-semismooth Newton methods for solving nonsmooth equations localized from these generalized equations. This new understanding expands the breadth of G-semismooth Newton methods in theory, results in a few interesting problems regarding the two categories of nonsmooth Newton methods, and more importantly, provides informative observations in facilitating the design and implementation of practical Newton-type algorithms for solving generalized equations.