First order optimality conditions for generalized semi-infinite programming problems

被引：28

作者：

Ye, J. J. ^{[1
]}

Wu, S. Y. ^{[2
,3
]}

机构：

[1] Univ Victoria, Dept Math & Stat, Victoria, BC, Canada

[2] Natl Cheng Kung Univ, Inst Appl Math, Tainan 700, Taiwan

[3] Natl Ctr Theoret Sci, Tainan, Taiwan

来源：

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS | 2008年 / 137卷 / 02期

基金：

加拿大自然科学与工程研究理事会;

关键词：

necessary optimality conditions; constraint qualifications; nonsmooth analysis; value function; generalized semi-infinite programming problems;

D O I：

10.1007/s10957-008-9352-z

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：

We study first-order optimality conditions for the class of generalized semi-infinite programming problems (GSIPs). We extend various well-known constraint qualifications for finite programming problems to GSIPs and analyze the extent to which a corresponding Karush-Kuhn-Tucker (KKT) condition depends on these extensions. It is shown that in general the KKT condition for GSIPs takes a weaker form unless a certain constraint qualification is satisfied. In the completely convex case where the objective of the lower-level problem is concave and the constraint functions are quasiconvex, we show that the KKT condition takes a sharper form.

引用

页码：419 / 434

页数：16

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