一类集值映射的方向度量次正则性  

Directional metric subregularity of a class of set-valued mappings

作　　者：黄远润 何青海 HUANG Yuan-run;HE Qing-hai(School of Mathematics and Statistics,Yunnan University,Kunming 650500,Yunnan,China)

机构地区：[1]云南大学数学与统计学院,云南昆明650500

出　　处：《云南大学学报（自然科学版）》2023年第2期266-275,共10页Journal of Yunnan University(Natural Sciences Edition)

基　　金：国家自然科学基金(12061085,11061039);云南省科技厅应用基础研究计划(202001BB050036,202201AT070066).

摘　　要：在有限维Hilbert空间中,研究连续可微单值映射与连续闭凸集值映射之差的集值映射的度量次正则性问题.首先,在适当的连续性假设条件下,得到了这类集值映射的强度量次正则性的充分条件;然后,研究了这类集值映射在存在某种“单值选择”条件下的方向度量次正则性,并给出了这类集值映射的方向度量次正则性的一些充分条件.In finite dimensional Hilbert space,the metric subregularity of a set-valued mapping,which is the difference of a continuous differentiable single valued mapping and a continuous closed convex set-valued mapping,is mainly analyzed.Firstly,under the appropriate continuous assumption,a sufficient condition for the strong metric subregularity of this kind of set-valued mappings is obtained;then,under the continuous condition of some“single value selection”,the directional metric subregularity of this type of set-valued mappings are explored,and some sufficient conditions for the directional metric subregularity of this kind of set-valued mappings are obtained.

关 键 词：集值映射 度量次正则性 切锥 法锥 

分 类 号：O177.92[理学—数学]