集值映射的Michel-Penot方向导数与Michel-Penot次微分  

Michel-Penot directional derivative and Michel-Penot subdifferentiation of set-valued mappings

作　　者：黄辉[1] 陈智勇 HUANG Hui;CHEN Zhiyong(School of Mathematics and Statistics,Yunnan University,Kunming 650091,Yunnan,China)

机构地区：[1]云南大学数学与统计学院,云南昆明650091

出　　处：《云南大学学报（自然科学版）》2024年第5期819-828,共10页Journal of Yunnan University(Natural Sciences Edition)

基　　金：国家自然科学基金(12061085).

摘　　要：采用标量化方法,研究集值映射的方向导数和次微分.借助Gerstewizt函数,给出了集值映射的Michel-Penot方向导数和Michel-Penot次微分的概念,研究了它们的性质,建立了它们的计算法则,并利用Michel-Penot次微分给出了无约束集值优化问题的优化条件.The directional derivatives and subdifferentials of set-valued mappings are studied by scalarization approaches.With the help of the Gerstewizt function,the concepts of Michel-Penot directional derivatives and Michel-Penot subdifferentials of set-valued mappings are introduced.Their properties are studied and their calculus rules are established.As application,optimality conditions for unconstrained set-valued optimization problems are given by Michel-Penot subdifferentials.

关 键 词：Michel-Penot方向导数 Michel-Penot次微分 集值映射 优化条件 

分 类 号：O221.6[理学—运筹学与控制论]