华东师范大学学报(自然科学版) ›› 2018, Vol. 2018 ›› Issue (1): 17-23.doi: 10.3969/j.issn.1000-5641.2018.01.003

• 数学 • 上一篇    下一篇

集值隐函数的似-Lipschitz性和相依导数

王丽娜1, 方志苗2, 李明华3   

  1. 1. 重庆水利电力职业技术学院, 重庆 402160;
    2. 重庆警察学院 基础教研部, 重庆 401331;
    3. 重庆文理学院 数学与财经学院, 重庆 402160
  • 收稿日期:2016-12-21 出版日期:2018-01-25 发布日期:2018-01-11
  • 作者简介:王丽娜,女,硕士,讲师,研究方向为最优化理论及应用.E-mail:lnw419@163.com.
  • 基金资助:
    重庆市教委科学技术研究项目，（KJ1601102，KJ1501503）；重庆市基础科学与前沿技术研究项目（cstc2016jcyjA0141，cstc2016jcyjA0270）；重庆文理学院科学研究基金（R2016SC13）

Lipschitz-likeness and contingent derivative of an implicit multifunction

WANG Li-na1, FANG Zhi-miao2, LI Ming-hua3   

  1. 1. Chongqing Water Resources and Electric Engineering College, Chongqing 402160, China;
    2. Department of Basic Courses, Chongqing Police College, Chongqing 401331, China;
    3. College of Mathematics and Finance, Chongqing University of Arts and Sciences Chongqing 402160, China
  • Received:2016-12-21 Online:2018-01-25 Published:2018-01-11

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摘要： 通过引入关键性假设，证明关键性假设与集值隐函数的Robinson度量正则性等价，并且在适当条件下证明了这个关键性假设是集值隐函数的似-Lipschitz性的充分条件.最后建立了集值函数的相依导数和二阶相依导数表达式.

关键词: 集值隐函数, Robinson度量正则性, 似-Lipschitz性, 相依导数

Abstract: In this paper by introducing a key assumption, we prove that the key assumption is equivalent to the Robinson metric regularity of the implicit multifunction and that under some suitable conditions the key assumption is sufficient for the Lipschitz-likeness (metric regularity) of the implicit multifunction. Finally, we establish the specific expressions of the contingent derivative and the second-order contingent derivative for the implicit multifunction.

Key words: implictit multifunction, Robinson metric regularity, Lipschitz-likeness, contingent derivative

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