Quadratic growth and critical point stability of semi-algebraic functions

• 成果类型: Article
• 署名作者: Drusvyatskiy, D.; Ioffe, A. D.
• 署名单位: University of Washington; University of Washington Seattle; Technion Israel Institute of Technology
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-014-0820-y
• 发表日期: 2015
• 页码: 635-653
• 关键词: metric regularity; tilt stability

摘要

We show that quadratic growth of a semi-algebraic function is equivalent to strong metric subregularity of the subdifferential-a kind of stability of generalized critical points. In contrast, this equivalence can easily fail outside of the semi-algebraic setting. As a consequence, we derive necessary conditions and sufficient conditions for optimality in subdifferential terms.