Separation theorems for nonconvex sets and application in optimization

被引：6
|
作者：
Kasimbeyli, Refail [1 ]
Karimi, Masoud [2 ]
机构：
[1] Eskisehir Tech Univ, Dept Ind Engn, Iki Eylul Campus, TR-26555 Eskisehir, Turkey
[2] Razi Univ, Dept Math, Kermanshah, Iran
来源：
OPERATIONS RESEARCH LETTERS | 2019年 / 47卷 / 06期
关键词：
Nonlinear separation theorem; Augmented dual cones; Nonconvex optimization; VECTOR OPTIMIZATION; SCALARIZATION; NONSMOOTH;
D O I：
10.1016/j.orl.2019.09.011
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：
The aim of this paper is to present separation theorems for two disjoint closed sets, without convexity condition. First, a separation theorem for a given closed cone and a point outside from this cone, is proved and then it is used to prove a separation theorem for two disjoint sets. Illustrative examples are provided to highlight the important aspects of these theorems. An application to optimization is also presented to prove optimality condition for a nonconvex optimization problem. (C) 2019 Elsevier B.V. All rights reserved.
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页码：569 / 573
页数：5
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