Subdifferentials at infinity and applications in optimization

• 成果类型: Article
• 署名作者: Kim, Do Sang; Nguyen, Minh Tung; Pham, Tien-Son
• 署名单位: Pukyong National University; Ho Chi Minh University of Banking (HUB); Dalat University
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610; 1436-4646
• DOI: 10.1007/s10107-024-02187-9
• 发表日期: 2025-11
• 页码: 409-440
• 关键词: Subdifferentials at infinity; optimality conditions; weak sharp minima; STABILITY; Lipschitzness at infinity

摘要

In this work, the notions of normal cones at infinity to unbounded sets and limiting and singular subdifferentials at infinity for extended real value functions are introduced. Various calculus rules for these notions are established. A complete characterization of the Lipschitz continuity at infinity for lower semicontinuous functions is given. The obtained results are aimed ultimately at applications to diverse problems of optimization, such as optimality conditions, coercive properties, weak sharp minima and stability results.