Well-posedness for set optimization problems

被引：90

作者：

Zhang, W. Y. ^{[1
]}

Li, S. J. ^{[1
]}

Teo, K. L. ^{[2
]}

机构：

[1] Chongqing Univ, Coll Math & Sci, Chongqing 400044, Peoples R China

[2] Curtin Univ Technol, Dept Math & Stat, Perth, WA 6845, Australia

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2009年 / 71卷 / 09期

基金：

中国国家自然科学基金;

关键词：

Well-posedness; Set optimization; Gerstewitz's function; VARIATIONAL PRINCIPLE; VECTOR OPTIMIZATION; VALUED OPTIMIZATION; MAPS; SCALARIZATION;

D O I：

10.1016/j.na.2009.02.036

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, three kinds of well-posedness for set optimization are first introduced. By virtue of a generalized Gerstewitz's function, the equivalent relations between the three kinds of well-posedness and the well-posedness of three kinds of scalar optimization problems are established, respectively. Then, sufficient and necessary conditions of well-posedness for set optimization problems are obtained by using a generalized forcing function, respectively. Finally, various criteria and characterizations of well-posedness are given for set optimization problems. (C) 2009 Elsevier Ltd. All rights reserved

引用

页码：3769 / 3778

页数：10

共 20 条

[1] Set-relations and optimality conditions in set-valued maps [J].

Alonso, M ;

Rodríguez-Marín, L .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2005, 63 (08) :1167-1179

[2]

Bednarczuk E., 1994, Control and Cybernetics, V23, P107

[3]

DENTCHEVA D, 1996, JOTA, V89, P329

[4]

Dontchev AL, 1993, LECT NOTES MATH, V1543

[5]

GOPFORT A, 2003, VARIATIONAL METHODS

[6] Some variants of the Ekeland variational principle for a set-valued map [J].

Ha, TXD .

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2005, 124 (01) :187-206

[7] Nonconvex scalarization in set optimization with set-valued maps [J].

Hernandez, E. ;

Rodriguez-Marin, L. .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2007, 325 (01) :1-18

[8] Set-valued increasing-along-rays maps and well-posed set-valued star-shaped optimization [J].

Hu, Rong ;

Fang, Ya-Ping .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2007, 331 (02) :1371-1383

[9] Levitin-Polyak well-posedness in generalized variational inequality problems with functional constraints [J].

Huang, X. X. ;

Yang, X. Q. .

JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION, 2007, 3 (04) :671-684

[10] Extended and strongly extended well-posedness of set-valued optimization problems [J].

Huang, XX .

MATHEMATICAL METHODS OF OPERATIONS RESEARCH, 2001, 53 (01) :101-116

← 1 2 →