集值隐函数的似-Lipschitz性和相依导数  

Lipschitz-likeness and contingent derivative of an implicit multifunction

作　　者：王丽娜[1] 方志苗[2] 李明华 WANG Li-na;FANG Zhi-miao;LI Ming-hua(Chongqing Water Resources and Electric Engineering College, Chongqing 402160, China;Department of Basic Courses, Chongqing Police College, Chongqing 401331, China;College of Mathematics and Finance, Chongqing University of Arts and Sciences,Chongqing 402160, China)

机构地区：[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

出　　处：《华东师范大学学报（自然科学版）》2018年第1期17-23,共7页Journal of East China Normal University(Natural Science)

基　　金：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)

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.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 Lipschitzlikeness(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.

关 键 词：集值隐函数 Robinson度量正则性 似-Lipschitz性 相依导数 

分 类 号：O224[理学—运筹学与控制论]