凸函数的支撑凸集及其集映射  

SUPPORT CONVEX SETS AND SET MAPPINGS FOR CONVEX FUNCTIONS

作　　者：陈少白[1] 王文义[2] 毛宗源[1] 

机构地区：[1]华南理工大学自动化科学与工程学院 [2]武汉船舶职业技术学院电子电气工程系,湖北武汉430050

出　　处：《数学杂志》2006年第5期585-590,共6页Journal of Mathematics

摘　　要：本文研究了线性空间中凸函数的支撑泛函存在性以及支撑泛函的数值域,利用子空间中支撑泛函延拓的方法,构造出在线性空间任意点的支撑泛函,确定在同一支撑点上支撑泛函的数值域,从而得到支撑泛函具有唯一性的充分必要条件,最后对支撑凸集到支撑泛函集的集映射进行讨论.This paper investigates existence of support functional of a convex function in linear spaces and the numerical ranges of the support functionals on a point. We construct support functionals with function extension and establish the numerical ranges of all support functionals on a support point. We present a necessary and sufficient condition for the support functional on a support point being unique. Finally, we discuss set mappings from support convex sets to support function sets.

关 键 词：凸函数 支撑泛函 数值域 集映射 

分 类 号：O174.51[理学—数学]