Coderivative-Based Newton Methods in Structured Nonconvex and Nonsmooth Optimization

• 成果类型: Article; Early Access
• 署名作者: Khanh, Pham Duy; Mordukhovich, Boris S.; Phat, Vo Thanh
• 署名单位: Wayne State University; University of North Dakota Grand Forks
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610; 1436-4646
• DOI: 10.1007/s10107-026-02420-7
• 发表日期: 2026-09-03
• 关键词: nonsmooth optimization; variational analysis; Generalized Newton methods; local convergence; GLOBAL CONVERGENCE; Nonconvex structured optimization; VARIATIONAL CONVEXITY; metric regularity; tilt stability; optimality conditions; algorithms; SUM

摘要

This paper proposes and develops new Newton-type methods to solve structured nonconvex and nonsmooth optimization problems with justifying their fast local and global convergence by means of advanced tools of variational analysis and generalized differentiation. The objective functions belong to a broad class of prox-regular functions with specification to constrained optimization of nonconvex structured sums. We also develop a novel line search method, which is an extension of the proximal gradient algorithm while allowing us to globalize the proposed coderivative-based Newton methods by incorporating the machinery of forward-backward envelopes. Applications and numerical experiments, which are provided for nonconvex least squares regression models, Student's t-regression with an & ell;0 -penalty, and image restoration problems, demonstrate the efficiency of the proposed algorithms.