REPRESENTATION OF BOUNDED CONVEX-SETS BY RATIONAL CONVEX-HULL OF ITS GAMMA-EXTREME POINTS

被引：5

作者：

PHU, HX ^{[1
]}

机构：

[1] INST MATH,HANOI 10000,VIETNAM

来源：

NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION | 1994年 / 15卷 / 7-8期

关键词：

BOUNDED CONVEX SETS; EXTREME POINTS; GAMMA-EXTREME POINTS; CONVEX HULL; RATIONAL CONVEX HULL;

D O I：

10.1080/01630569408816600

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

H. Minkowski proved C = conv ext C whenever C is a compact convex subset of a finite-dimensional linear space. If C is bounded but not closed, this representation does not hold anymore. In this case, we introduce the set of so-called gamma-extreme points ext(gamma)C of C and show C = conv ext(gamma)C = raco ext(gamma)C, where raco M denotes the rational convex hull of M.

引用

页码：915 / 920

页数：6