集值映射的(C,ε)-超次微分和集值优化问题的最优性条件  

(C,ε)-Super Subdifferentials of Set-Valued Maps and Optimality Conditions for Set-Valued Optimization Problems

作　　者：周志昂 杨爽 Zhi Ang ZHOU;Shuang YANG(College of Sciences,Chongqing University of Technology,Chongqing 400054,P.R.China)

机构地区：[1]重庆理工大学理学院,重庆400054

出　　处：《数学学报（中文版）》2022年第5期859-876,共18页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金(12171061,11861002);重庆市教委科学技术研究计划(KJZD-K202001104)。

摘　　要：本文研究了集值映射的(C,ε)-超次微分.首先,引进了集合的(C,ε)-超有效点,呈现了(C,ε)-超有效点的一些性质和等价刻画,在(C,ε)-超有效性意义下,获得了集值优化问题的标量化定理.其次,定义了集值映射的(C,ε)-超次微分,研究了(C,ε)-超次微分的存在条件,建立了用(C,ε)-超次微分刻画的Moreau-Rockafellar定理.最后,作为应用,建立了涉及(C,ε)-超次微分的集值优化问题的最优性条件.本文获得的结果统一和推广了一些文献中用超次微分或ε-超次微分刻画的结果.In this paper,we study(C,ε)-super subdifferentials of set-valued maps.First,we introduce a notion of(C,ε)-super efficient point of a set.Some properties and equivalent characterizations of the(C,ε)-super efficient points are presented.Scalarization theorems of the set-valued optimization problem are obtained in the sense of(C,ε)-super efficiency.Second,we define(C,ε)-subdifferentials of set-valued maps and research the existence conditions of(C,ε)-subdifferentials.Moreau-Rockafellar type theorems characterized by(C,ε)-subdifferentials are also established.Finally,as the applications,we establish some optimality conditions of the set-valued optimization problem involving the(C,ε)-super subdifferentials.The results obtained in this paper unify and generalize some results characterized by the super subdifferentials or ε-super subdifferentials of the set-valued maps in the literature.

关 键 词：集值映射 近似(C ε)-次似凸 (C ε)-超次微分 最优性条件 

分 类 号：O221.6[理学—运筹学与控制论]