General Ekeland's variational principle for set-valued mappings

被引：38

作者：

Chen, GY ^{[1
]}

Huang, XX

Hou, SH

机构：

[1] Acad Sinica, Inst Syst Sci, Beijing 100080, Peoples R China

[2] Chongqing Normal Univ, Dept Math & Comp Sci, Chongqing, Peoples R China

[3] Hong Kong Polytech Univ, Dept Math Appl, Hong Kong, Hong Kong, Peoples R China

来源：

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS | 2000年 / 106卷 / 01期

关键词：

set-valued optimization; variational principle; Hausdorff maximality principle;

D O I：

10.1023/A:1004663208905

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 paper, we introduce the concept of approximate solutions for set-valued optimization problems. A sufficient condition for the existence of approximate solutions is obtained. A general Ekeland's variational principle for set-valued mappings in complete ordered metric spaces and complete metric spaces are derived. These results are generalizations of results for vector-valued functions in Refs. 1-4.

引用

页码：151 / 164

页数：14

共 9 条

[1] Aubin J.-P., 1984, Differential Inclusions
[2] A unified approach to the existing three types of variational principles for vector valued functions
Chen, GY
Huang, XX
[J]. MATHEMATICAL METHODS OF OPERATIONS RESEARCH, 1998, 48 (03) : 349 - 357
[3] DENTCHEVA D, 1996, JOTA, V89, P329
[4] DUNFORD N, 1958, LINEAR OPERATIORS, V1
[5] ON PROPERTY (Q) AND OTHER SEMICONTINUITY PROPERTIES OF MULTIFUNCTIONS
HOU, SH
[J]. PACIFIC JOURNAL OF MATHEMATICS, 1982, 103 (01) : 39 - 56
[6] ISAC G, 1996, LECT NOTES EC MATH S, V432, P148
[7] A NONCONVEX VECTOR MINIMIZATION PROBLEM
NEMETH, AB
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1986, 10 (07) : 669 - 678
[8] Sawaragi Y., 1985, THEORY MULTIOBJECTIV
[9] Tammer C., 1992, Optimization, V25, P129, DOI 10.1080/02331939208843815

← 1 →