Gap functions for a system of generalized vector quasi-equilibrium problems with set-valued mappings

被引：22

作者：

Huang, Nan-Jing ^{[2
]}

Li, Jun ^{[3
]}

Wu, Soon-yi ^{[1
,4
]}

机构：

[1] Natl Cheng Kung Univ, Inst Appl Math, Tainan 700, Taiwan

[2] Sichuan Univ, Dept Math, Chengdu 610064, Sichuan, Peoples R China

[3] China W Normal Univ, Sch Math & Informat, Nanchong 637002, Sichuan, Peoples R China

[4] Natl Ctr Theoret Sci, Tainan, Taiwan

来源：

JOURNAL OF GLOBAL OPTIMIZATION | 2008年 / 41卷 / 03期

基金：

中国国家自然科学基金; 高等学校博士学科点专项科研基金;

关键词：

system of generalized vector quasi-equilibrium problems; gap function; nonlinear scalarization function; set-valued mapping;

D O I：

10.1007/s10898-007-9248-8

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, some gap functions for three classes of a system of generalized vector quasi-equilibrium problems with set-valued mappings (for short, SGVQEP) are investigated by virtue of the nonlinear scalarization function of Chen, Yang and Yu. Three examples are then provided to demonstrate these gap functions. Also, some gap functions for three classes of generalized finite dimensional vector equilibrium problems (GFVEP) are derived without using the nonlinear scalarization function method. Furthermore, a set-valued function is obtained as a gap function for one of (GFVEP) under certain assumptions.

引用

页码：401 / 415

页数：15

共 36 条

[1] The system of generalized vector equilibrium problems with applications [J].

Ansari, QH ;

Schaible, S ;

Yao, JC .

JOURNAL OF GLOBAL OPTIMIZATION, 2002, 22 (1-4) :3-16

[2] The system of vector quasi-equilibrium problems with applications [J].

Ansari, QH ;

Chan, WK ;

Yang, XQ .

JOURNAL OF GLOBAL OPTIMIZATION, 2004, 29 (01) :45-57

[3] Characterizations of solutions for vector equilibrium problems [J].

Ansari, QH ;

Konnov, IV ;

Yao, JC .

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2002, 113 (03) :435-447

[4] An existence result for the generalized vector equilibrium problem [J].

Ansari, QH ;

Yao, JC .

APPLIED MATHEMATICS LETTERS, 1999, 12 (08) :53-56

[5] Vector equilibrium problems with generalized monotone bifunctions [J].

Bianchi, M ;

Hadjisavvas, N ;

Schaible, S .

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 1997, 92 (03) :527-542

[6]

Blum E., 1994, MATH STUDENT, V63, P127

[7] Equilibrium problems with applications to eigenvalue problems [J].

Chadli, O ;

Wong, NC ;

Yao, JC .

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2003, 117 (02) :245-266

[8] A nonlinear scalarization function and generalized quasi-vector equilibrium problems [J].

Chen, GY ;

Yang, XQ ;

Yu, H .

JOURNAL OF GLOBAL OPTIMIZATION, 2005, 32 (04) :451-466

[9] Characterizations of variable domination structures via nonlinear scalarization [J].

Chen, GY ;

Yang, XQ .

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 2002, 112 (01) :97-110

[10]

Chen GY, 2005, LECT NOTES ECON MATH, V541, P1, DOI 10.1007/3-540-28445-1

← 1 2 3 4 →