Links between directional derivatives through multidirectional mean value inequalities

• 成果类型: Article; Proceedings Paper
• 署名作者: Correa, Rafael; Gajardo, Pedro; Thibault, Lionel
• 署名单位: Universidad Tecnica Federico Santa Maria; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universidad de Chile; Universite de Montpellier
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-007-0131-7
• 发表日期: 2009
• 页码: 57-77
• 关键词: banach-space; subdifferentials; tangent; Finite; sets

摘要

We prove in the general setting of lower semicontinuous functions on Banach spaces the relation between the Rockafellar directional derivative and the mixed lower limit of the lower Dini derivatives. As a byproduct we derive the famous inclusions of tangent cones of closed sets in Banach spaces. The results are established using as principal tool multidirectional mean value inequalities [Aussel et al., SIAM J Optim 9(3), 690-706 (1999)].