Weak Differentiability with Applications to Variational Analysis

作者：Wang, Bingwu^*; Yang, Xinmin

来源：Set-Valued and Variational Analysis, 2016, 24(2): 299-321.

DOI：10.1007/s11228-015-0341-8

• Differentiability
• beta-differentiability
• Weak differentiability
• Uniform weak differentiability
• Variational analysis
• Generalized differentiation
• Sequential normal compactness

In this paper we first review the theory of weak differentiability with some improvements and unifications of existing results; then we introduce an extended variant of this notion and establish its basic properties; finally we use the weak differentiability and its variant to develop new calculus results in variational analysis for the theory of generalized differentiation and the sequential normal compactness. In this way we demonstrate that the weak differentiability and its variant, in contrast to the usual differentiability, are in fact more suitable for Frechet and limiting/Mordukhovich constructions in variational analysis.

• 出版日期2016-6
• 单位重庆师范大学