广义向量混合拟平衡系统的间隙函数和解的存在性

数学物理学报 ›› 2011, Vol. 31 ›› Issue (6): 1637-1646.

广义向量混合拟平衡系统的间隙函数和解的存在性

谢静^1,2|何中全¹

1.西华师范大学数学与信息学院 |四川南充 637002|
2.连云港海州高级中学 |江苏连云港 222023

收稿日期:2009-10-08 修回日期:2011-04-06 出版日期:2011-12-25 发布日期:2011-12-25
基金资助:
四川省教育厅项目(08ZA159)资助

Gap Functions and Existence of Solutions to System of Generalized Vector Mixed Quasi-Equilibrium Problems

XIE Jing^1,2, HE Zhong-Quan¹

1.School of Mathematics and Information, China West Normal University, Sichuan Nanchong 637002;
2.Lianyungang Haizhou High School, Jiangsu Lianyungang 222023

Received:2009-10-08 Revised:2011-04-06 Online:2011-12-25 Published:2011-12-25
Supported by:
四川省教育厅项目(08ZA159)资助

摘要/Abstract

摘要：

该文引入了四类多值广义向量混合拟平衡系统, 研究了这些系统解的存在性. 借助非线性标量函数, 得到了这类系统的间隙函数.

关键词: 广义向量混合拟平衡系统, 非线性标量函数, 间隙函数

Abstract:

In this paper, we introduce four new types of the system of generalized vector mixed quasi-equilibrium problems with set-valued maps and establish their existence theorems. Then, by virtue of a nonlinear scalarization function, the gap functions for these problems are obtained.

Key words: System of generalized vector mixed quasi-equilibrium problems, Nonlinear scalarization function, Gap function

中图分类号:

74G25

谢静, 何中全. 广义向量混合拟平衡系统的间隙函数和解的存在性[J]. 数学物理学报, 2011, 31(6): 1637-1646.

XIE Jing, HE Zhong-Quan. Gap Functions and Existence of Solutions to System of Generalized Vector Mixed Quasi-Equilibrium Problems[J]. Acta mathematica scientia,Series A, 2011, 31(6): 1637-1646.

参考文献

[1] Ansari Q H, Chan W K, Yang X Q. The system of generalized vector equilibrium problems with applications. J Global Optim, 2004, 29: 45--57

[2] Ansari Q H, Konnov, I V, Yao J C. Existence of a solution and variational principles for vector equilibrium problems. J Optim Theory Appl, 2001, 110(3): 481--492

[3] Ansari Q H, Schaible S, Yao J C. The system of generalized vector equilibrium problems with applications. J Global Optim, 2002, 22: 3--16

[4] Ansari Q H, Schaible S, Yao J C. The system of vector equilibrium problems with applications. J Optim Theory Appl, 2000, 107(3): 547--557

[5] Ansari Q H, Yao J C. A fixed point theorem and its applications to a system of variational inequlities. Bull Australian Math Soc, 1999, 59(3): 433--442

[6] Ansari Q H, Yao J C. Systems of generalized variational inequlities and their applications. Bull Australian Math Soc, 2000, 76(3/4): 203--217

[7] Chen Y G, Yang X Q, Yu H. A nonlinear scalarization theorems and generalized vector quasi-equilibrium problems. J Global Optim, 2005, 32(4): 451--466

[8] Chen G Y, Goh C J, Yang X Q. The gap function of a convex multicriteria optimization problem. European J Oper Res, 1998, 111: 142--151

[9] Fu J Y. Vector equilibrium problems existence theorems and convexity of solution set. J Global Optim, 2005, 31: 109--119

[10] Fu J Y. Generalized vector quasi-equilibrium problemst. J Math Meth Oper Res, 2000, 52: 57--64

[11] Fu J Y, Wan A H. Generalized vector quasi-equilibrium problems with set-valued maps. J Math Meth Oper Res, 2002, 56: 259--268

[12] Fang M, Huang N J. A System of generalized mixed vector quasi-equilibrium problems in product FC-spaces. Math Sinica, 2007, 50(2): 291--298

[13] Fang M, Huang N J, Kim K J. Existence results for systems of vector equilibrium problems. J Global Optim, 2006, 35: 71--83

[14] Gerth C, Weidner P. Nonconvex separation theorems and some applications in vector optimization. J Optim Theory Appl, 1990, 67: 297--320

[15] Gong X. Strong vector equilibrium problems. J Global Optim, 2006, 36: 339--349

[16] Homidan S A, Ansari Q H, Schaible S. Existence of solutions of systems of generalized implicit vector variational inequalities. J Optim Theory Appl, 2007, 134: 515--531

[17] Hou H S, Yu H, Chen G Y. On vector quasi-equilibrium problems with set-valued maps. J Optim Theory Appl, 1990, 67: 297--320

[18] Lee B S, Lee G M, Lee S J. Variational-type inquelities for (η, θ,δ)-pseudomonotone-type set-valued in nonreflexive banach spaces.
J Optim Theory Appl, 2002, 15: 109--114

[19] Li J, Huang N J. An extension of gap functions for a system of vector equilibrium problems with applications to optimization problems.
J Global Optim, 2007, 39: 247--260

[20] Lin J L. System of generalized vector quasi-equilibrium problems with applications to fixed point theorems for a family of nonexpansive multivalued mappings. J Global Optim, 2006, 34: 15--32

[21] Lin L J, Yu Z T, Kassay G. Existence of equilibria for multivalued mappings and its application to vectorial equilibria. Journal of Optimization Theory Applications, 2002, 114(1): 189--208

[22] Li S J, Teo K L, Yang X Q, Wu S Y. Gap functions and existence of solutions to generalized vector quasi-equilibrium problems. J Global Optim, 2006, 34: 427--440

[23] Li S J, Teo K L, Yang X Q. Generalized vector quasi-equilibrium problems. Mathematical Methods of Operations Research, 2005, 61: 385--397

[24] Lin Z. The study of system of vector quasi-equilibrium problems. J Global Optim, 2006, 36: 627--635

[25] Mastroeni G. The study of system of vector quasi-equilibrium problems. J Global Optim, 2003, 27: 411--426

[26] Peng J W, Lee H W J, Yang X M. On system of generalized vector quasi-equilibrium problems with set-valued maps. J Global Optim, 2006, 36: 139--158

[27] Rouhani B D, Tarafdar E, Watson P J. Existence of solution to some equilibrium problems. J Optim Theory Appl, 2005, 126(1): 97--107

[28] Ding X P. System of generalized vector quasi-equilibrium problems on product Fc-spaces. Acta Mathematica Scientia, 2007, 27(3): 522--534

[29] Ding X P. Mathematical programs with system of generalized vector quasi-equilibrium constraints in Fc-spaces. Acta Mathematica Scientia, 2010, 20(4): 1257--1268