KKT conditions for weak* compact convex sets, theorems of the alternative, and optimality conditions

被引：1
|
作者：
Wu, Zili [1 ]
机构：
[1] Xian Jiaotong Liverpool Univ, Dept Math Sci, Suzhou 215123, Jiangsu, Peoples R China
来源：
JOURNAL OF FUNCTIONAL ANALYSIS | 2014年 / 266卷 / 02期
关键词：
Support functions; Theorems of the alternative; KKT conditions; Optimality conditions; Subdifferentials; OPTIMIZATION; EQUALITY; INEQUALITY; CONE;
D O I：
10.1016/j.jfa.2013.10.023
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We present several equivalent conditions for the Karush-Kuhn-Tucker conditions for weak* compact convex sets. Using them, we extend several existing theorems of the alternative in terms of weak* compact convex sets. Such extensions allow us to express the KKT conditions and hence necessary optimality conditions for more general nonsmooth optimization problems with inequality and equality constraints. Furthermore, several new equivalent optimality conditions for optimization problems with inequality constraints are obtained. (C) 2013 Elsevier Inc. All rights reserved.
引用
收藏
页码：693 / 712
页数：20
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