Local Maximal Monotonicity in Variational Analysis and Optimization

• 成果类型: Article; Early Access
• 署名作者: Khanh, Pham Duy; Khoa, Vu Vinh Huy; Mordukhovich, Boris S.; Phat, Vo Thanh
• 署名单位: Wayne State University; University of North Dakota Grand Forks
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2023.0270
• 发表日期: 2025
• 关键词: proximal point algorithm; convexity; Operators; STABILITY

摘要

The paper is devoted to a systematic study and characterizations of notions of local maximal monotonicity and their strong counterparts for set-valued operators that appear in variational analysis, optimization, and their applications. We obtain novel resolvent characterizations of these notions together with efficient conditions for their preservation under summation in broad infinite-dimensional settings. Further characterizations of these notions are derived by using generalized differentiation of variational analysis in the framework of Hilbert spaces.