Three criteria of minimality for pairs of compact convex sets

被引：3

作者：

Grzybowski, J. ^{[1
]}

Urbanski, R. ^{[1
]}

机构：

[1] Adam Mickiewicz Univ Poznan, Poznan, Poland

来源：

OPTIMIZATION | 2006年 / 55卷 / 5-6期

关键词：

convex analysis; convex polytope; pairs of convex sets;

D O I：

10.1080/02331930600816148

中图分类号：

C93 [管理学]; O22 [运筹学];

学科分类号：

070105 ; 12 ; 1201 ; 1202 ; 120202 ;

摘要：

In this article, we generalize the 'facets criterion' (Wiernowolski, M., 1994, A criterion for the minimality of pairs of convex compact sets. Commentationes Mathematicae, 34, 247-252) and give a new shorter proof of it (Theorem 1), formulate and prove the 'edges criterion' (Theorem 2) and generalize the 'steps criterion' (Pallaschke, D. and Urbaftski, R., 1993, Some criteria for the minimality of pairs of compact convex sets. Methods and Models of Operations Research (ZOR), 37, 129-150) (Theorem 3).

引用

页码：569 / 576

页数：8