对称向量拟均衡问题有效解的存在性

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  • 1. 宿迁高等师范学校数学系, 江苏宿迁 223800
    2. 南昌大学数学系, 南昌 330031
王秀玲 E-mail: wang_xiuxiu@163.com

收稿日期: 2019-02-19

  网络出版日期: 2021-03-05

基金资助

国家自然科学基金(11061023)

An existence theorem for efficient solutions of symmetric vector quasi-equilibrium problems

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  • 1. Department of Mathematics, Suqian Higher Normal School, Suqian 223800, Jiangsu, China
    2. Department of Mathematics, NanchangUniversity, Nanchang 330031, China

Received date: 2019-02-19

  Online published: 2021-03-05

摘要

利用标量化方法建立对称向量拟均衡问题有效解的存在性定理。作为标量化方法的应用,利用这一方法得到向量变分不等式和拟向量变分不等式有效解的存在性定理。

本文引用格式

王秀玲, 龚循华 . 对称向量拟均衡问题有效解的存在性[J]. 运筹学学报, 2021 , 25(1) : 73 -80 . DOI: 10.15960/j.cnki.issn.1007-6093.2021.01.006

Abstract

In this paper, an existence theorem for efficient solutions of symmetric vector quasi-equilibrium problems is established by using a scalarization method. As applications of the scalarization method, we use the scalarization method to obtain existence theorems for efficient solutions of vector variational inequality and vector quasi-variational inequality.

参考文献

1 Ansari Q H , Oettli W , Schi$\ddot{\rm{a}}$ger D . A generalization of vectorial equilibria[J]. Mathematical Methods of Operations Research, 1997, 46, 147- 152.
2 Ansari Q H , Konnov I V , Yao J C . Existence of a solution and variational principles for vector equilibrium problems[J]. Journal of Optimization Theory and Applications, 2001, 110, 481- 492.
3 Tan N X . On the existence of solutions of quasivariational inclusion problems[J]. Journal of Global Optimization, 2004, 123, 619- 638.
4 Fang X P , Huang N J . Strong vector variational inequalities in Banach spaces[J]. Applied Mathematics Letters, 2006, 19, 362- 368.
5 Long X J , Huang N J , Teo K L . Existence and stability of solutions for generalized strong vector quasi-equilibrium problem[J]. Computational Mathematics and Modeling, 2008, 47, 445- 451.
6 Hou S H , Gong X H , Yang X M . Existence and stability of solutions for generalized $y$ Fan inequality problems with trifunctions[[J]. Journal of Optimization Theory and Applications, 2010, 146, 387- 398.
7 Cap$\breve{\rm{a}}$t$\breve{\rm{a}}$ A . Existence results for proper efficient solutions of vector equilibrium problems and applications[J]. Journal of Global Optimization, 2011, 51, 657- 675.
8 Blum E , Oettli W . From optimization and variational inequalities to equilibrium problems[J]. Mathematics Student, 1994, 63, 123- 145.
9 Noor M A , Oettli W . On general nonlinear complementarity problems and quasiequilibria[J]. Le Matematiche XLLX, 1994, 49, 313- 331.
10 Fu J Y . Symmetric vector quasi-equilibrium problems[J]. Journal of Mathematical Analysis and Applications, 2003, 285, 708- 713.
11 Farajzadeh A P . On the symmetric vector quasi-equilibrium problems[J]. Journal of Mathematical Analysis and Applications, 2006, 322, 1099- 1110.
12 Chen J C , Gong X H . The stability of set of solutions for symmetric vector quasi-equilibrium problems[J]. Journal of Global Optimization, 2008, 136, 359- 374.
13 Gong X H . Symmetric strong vector quasi-equilibrium problems[J]. Mathematical Methods of Operations Research, 2007, 65, 305- 314.
14 Tanaka T . Generalized quasiconvexities, cone saddle points, and minimax theorem for vector-valued functions[J]. Journal of Optimization Theory and Applications, 1994, 81, 355- 377.
15 Ferro F . A minimax theorem for vector-valued functions[J]. Journal of Optimization Theory and Applications, 1989, 60, 19- 31.
16 G$\ddot{\rm{o}}$pfert A , Riahi H , Tammer C , et al. Variational Methods in Partially Ordered Spaces[M]. New York: Springer, 2003.
17 张石生. 变分不等式及其相关问题[M]. 重庆: 重庆出版社, 2008.
18 Browder F E . A new generalization of the Schauder fixed point theorem[J]. Annals of Mathematics, 1967, 174, 285- 290.
19 Aubin J P , Ekeland I . Applied Nonlinear Analysis[M]. New York: John Wiley and Sons, 1984.
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