华东师范大学学报（自然科学版） >

2018 , Vol. 2018 >Issue 1: 17 - 23

DOI: https://doi.org/10.3969/j.issn.1000-5641.2018.01.003

数学

集值隐函数的似-Lipschitz性和相依导数

  • 王丽娜 ,
  • 方志苗 ,
  • 李明华
展开
  • 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
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.

收稿日期: 2016-12-21

  网络出版日期: 2018-01-11

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）

收起

Lipschitz-likeness and contingent derivative of an implicit multifunction

  • WANG Li-na ,
  • FANG Zhi-miao ,
  • LI Ming-hua
Expand
  • 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 date: 2016-12-21

  Online published: 2018-01-11

Fold

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

本文引用格式

王丽娜 , 方志苗 , 李明华 . 集值隐函数的似-Lipschitz性和相依导数[J]. 华东师范大学学报（自然科学版）, 2018 , 2018(1) : 17 -23 . DOI: 10.3969/j.issn.1000-5641.2018.01.003

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

参考文献

[1] ZHAO J. The lower semicontinuity of optimal solution sets[J]. J Math Anal Appl, 1997, 207:240-254.
[2] KIEN B T. On the lower semicontinuity of optimal solution sets[J]. Optimization, 2005, 54:123-130.
[3] LI S J, CHEN C R. Stability of weak vector variational inequality[J]. Nonlinear Analysis Theory Methods & Applications, 2009, 70:1528-1535.
[4] CHEN C R, LI S J, FANG Z M. On the solution semicontinuity to a parametric generalized vector quasivariational inequality[J]. Comput Math Appl, 2010, 60:2417-2425.
[5] ZHONG R Y, HUANG N J. Lower semicontinuity for parametric weak vector variational inequalities in reflexive Banach spaces[J]. J Optimiz Theory App, 2011, 150:317-326.
[6] ROCKAFELLAR P T, WETS R J B. Variational Analysis[M]. Berlin:Springer, 1998.
[7] ROBINSON S M. Generalized equations and their solutions, part I:Basic theory[J]. Math Program Study, 1979, 10:128-141.
[8] BONNANS J F, SHAPIRO A. Perturbation Analysis of Optimization Problems[M]. New York:Springer, 2000.
[9] AUBIN J P, EKELAND I. Applied Nonlinear Analysis[M]. New York:John Wiley and Sons, 1984.
[10] AUBIN J P, FRANKOWSKA H. Set-Valued Analysis[M]. Boston:Birkhauser, 1990.
Options
文章导航

/

〈 〉