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

[11] Pointwise well-posedness of perturbed vector optimization problems in a vector-valued variational principle [J].

Huang, XX .

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2001, 108 (03) :671-684

[12]

Kuroiwa D., 2003, Journal of Information & Optimization Sciences, V24, P73, DOI 10.1080/02522667.2003.10699556

[13] On set-valued optimization [J].

Kuroiwa, D .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2001, 47 (02) :1395-1400

[14]

Kuroiwa D., 1999, Nonlinear Analysis and Convex Analysis, P221

[15]

Kuroiwa D., 2003, J. Nonlinear Convex Anal., V84, P117

[16] Well-posedness and L-well-posedness for quasivariational inequalities [J].

Lignola, MB .

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2006, 128 (01) :119-138

[17]

Lucchetti R., 1995, Recent Developments in Well-posed Variational Problems

[18] Well-posedness and scalarization in vector optimization [J].

Miglierina, E ;

Molho, E ;

Rocca, M .

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2005, 126 (02) :391-409

[19] Well-posed vector optimization problems and vector variational inequalities [J].

Rocca, Matteo .

JOURNAL OF INFORMATION & OPTIMIZATION SCIENCES, 2006, 27 (02) :259-270

[20]

Tykhonov AN., 1966, COMP MATH MATH PHYS+, V6, P28, DOI [10.1016/0041-5553(66)90003-6, DOI 10.1016/0041-5553(66)90003-6]

← 1 2 →