A nonsmooth Robinson's inverse function theorem in Banach spaces

• 成果类型: Article
• 署名作者: Cibulka, R.; Dontchev, A. L.
• 署名单位: University of West Bohemia Pilsen; University of West Bohemia Pilsen; University of Michigan System; University of Michigan; University of Michigan System; University of Michigan
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-015-0877-2
• 发表日期: 2016
• 页码: 257-270
• 关键词: implicit-function theorem

摘要

In a recent paper, Izmailov (Math Program Ser A 147:581-590, 2014) derived an extension of Robinson's implicit function theorem for nonsmooth generalized equations in finite dimensions, which reduces to Clarke's inverse function theorem when the generalized equation is just an equation. Pales (J Math Anal Appl 209:202-220, 1997) gave earlier a generalization of Clarke's inverse function theorem to Banach spaces by employing Ioffe's strict pre-derivative. In this paper we generalize both theorems of Izmailov and Pales to nonsmooth generalized equations in Banach spaces.