引用本文:肖成英, 杨明歌.Banach空间中集值隐函数的类Lipschitz性质及其应用[J].西南师范大学学报(自然科学版),2019,44(7):17~22
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Banach空间中集值隐函数的类Lipschitz性质及其应用
肖成英, 杨明歌1,2
1. 四川工商学院 云计算与智能信息处理重点实验室, 成都 611745;2. 上海大学 管理学院, 上海 200444
摘要:
利用变分分析和广义微分的相关工具,在Banach空间中研究集值隐函数的稳定性,给出集值隐函数在给定点具有类Lipschitz性质的Clarke上导数充分条件.作为应用,讨论参数向量优化问题有效解映射的稳定性,给出有效解映射在给定点具有类Lipschitz性质的Clarke上导数充分条件.所得结果改进了相关文献中的结果.
关键词:  集值隐函数  稳定性分析  参数向量优化问题  有效解映射  类Lipschitz性质
DOI:10.13718/j.cnki.xsxb.2019.07.003
分类号:O224
基金项目:国家自然科学基金项目(11801352);四川省教育厅科研项目(17ZB0265).
Lipschitz-Like Property of Implicit Multifunctions in Banach Spaces and Applications
XIAO Cheng-ying, YANG Ming-ge1,2
1. Key Laboratory of Cloud Computing and Intelligent Information Processing, Sichuan Technology and Business University, Chengdu 611745, China;2. School of Management, Shanghai University, Shanghai 200444, China
Abstract:
In this paper, by means of variational analysis and generalized differentiation, we study the stability of implicit multifunctions in Banach spaces, and give sufficient conditions in terms of Clarke coderivative to show that the implicit multifunction is Lipschitz-like at the given point. As applications, we discuss the stability of parametric vector optimization problems, and provide sufficient conditions in terms of Clarke coderivative for guaranteeing the efficient solution map to be Lipschitz-like at the given point. The results obtained in this paper improve the corresponding results in the literature.
Key words:  implicit multifunction  stability analysis  parametric vector optimization problem  efficient solution map  Lipschitz-like property
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