参数弱向量平衡问题解集映射的连续性

doi:10.15960/j.cnki.issn.1007-6093.2016.01.012

运筹学学报

参数弱向量平衡问题解集映射的连续性

罗国旺^1,* 彭艳芳² 刘衍民¹ 黄建文¹

1. 遵义师范学院数学与计算科学学院, 贵州遵义 563002; 2. 贵州师范大学数学与计算机科学学院, 贵阳 550001

收稿日期:2014-10-24 出版日期:2016-03-15 发布日期:2016-03-15
通讯作者: 罗国旺 lgwangw@163.com
基金资助:
国家自然科学基金(No. 71461027), 贵州省科学技术基金(No. 黔科合J字LKS[2013]03号), 贵州省科技合作计划课题(No. 黔科合LH字[2015]7055号)

Continuity of the solution set map to parametric weak vector equilibrium problems

LUO Guowang^1,*PENG Yanfang²LIU Yanmin¹HUANG Jianwen¹

1. School of Mathematics and Computational Science, Zunyi Normal College, Zunyi 563002, Guizhou, China; 2. School of Mathematics and Computer Science, Guizhou Normal University, Guiyang 550001, China

Received:2014-10-24 Online:2016-03-15 Published:2016-03-15

摘要/Abstract

摘要：

运用非线性标量化方法, 讨论参数弱向量平衡问题解集映射的上半连续性和下半连续性, 并举例说明了所得结果的正确性.

关键词: 参数弱向量平衡问题, 上半连续性, 下半连续性, 非线性标量化

Abstract:

In this paper, using the nonlinear scalarization method, we obtain the upper semicontinuity and lower semicontinuity of the solution mappings to parametric weak vector equilibrium problems. Some examples are given to illustrate our results.

Key words: parametric weak vector equilibrium problem, upper semicontinuity, lower semicontinuity, nonlinear scalarization

罗国旺, 彭艳芳, 刘衍民, 黄建文. 参数弱向量平衡问题解集映射的连续性[J]. 运筹学学报, doi: 10.15960/j.cnki.issn.1007-6093.2016.01.012.

LUO Guowang, PENG Yanfang, LIU Yanmin, HUANG Jianwen. Continuity of the solution set map to parametric weak vector equilibrium problems[J]. Operations Research Transactions, doi: 10.15960/j.cnki.issn.1007-6093.2016.01.012.

参考文献

[1] Li S J, Chen G Y, Teo K L. On the stability of generalized vector quasivariational inequality problems [J]. Journal of Optimization Theory and Applications, 2002, 113: 283-295.

[2] Huang N J, Li J, Thompson H B. Stability for parametric implicit vector equilibrium problems [J]. Decisions in Economics and Finance, 2006, 43: 1267-1274.

[3] Gong X H. Continuity of the solution set to parametric weak vector equilibrium problems [J]. Journal of Optimization Theory and Applications, 2008, 139: 35-46.

[4] Chen C R, Li S J, Teo K L. Solution semicontinuity of parametric generalized vector equilibrium problems [J]. Journal of Global Optimization, 2009, 45: 309-318.

[5] Li S J, Fang Z M. Lower semicontinuity of the solution mappings to a parametric generalized Ky Fan inequality [J]. Journal of Optimization Theory and Applications, 2010, 147: 507-515.

[6] Peng Z Y, Yang X M, Peng J W. On the lower semicontinuity of the solution mappings to parametric weak generalized Ky Fan inequality [J]. Journal of Optimization Theory and Applications, 2012, 152: 256-264.

[7] Wangkeeree R, Wangkeeree R, Rreechasilp P. Continuity of the solution mappings to parametric generalized vector equilibrium problems [J]. Applied Mathematics Letters, 2014, 29: 42-45.

[8] Chen G Y, Huang X X, Yang X Q. Vector Optimization: Set-Valued and Variational Analysis [M]. Berlin: Springer, 2005.

[9] Chen G Y, Goh C J, Yang X Q. Vector network equilibrium problems and nonlinear scalarization methods [J]. Mathematical Methods of Operations Research, 1999, 49: 239-253.

[10] Chen G Y, Yang X Q, Yu H. A nonlinear scalarization function and generalized quasi-vector equilibrium problems [J]. Journal of Global Optimization, 2005, 32: 451-466.

[11] Chen C R, Li M H. Holder continuity of solutions to parametric vector equilibrium problems with nonlinear scalarization [J]. Numerical Functional Analysis and Optimization, 2014, 35: 685-707.

[12] Aubin J P, Ekeland I. Applied Nonlinear Analysis [M]. New York: John Wiley Sons, 1984.

[13] Luc D T. Theory of vector optimization [M]//Lecture Notes in Economics and Mathematical Systems, New York: Spring-Verlag, 1989.

[14] Wang S H, Li Q Y. A projection iterative algorithm for strong vector equilibrium problem [J]. Optimization, 2014, DOI: 10.1080/02331934.2014.919501.

[15] Chen C R, Li S J. On the solution continuity of parametric generalized systems [J]. Pacific Journal of Optimization, 2010, 6: 141-151.

参数弱向量平衡问题解集映射的连续性

Continuity of the solution set map to parametric weak vector equilibrium problems

PDF

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 4

编辑推荐

Metrics

本文评价

[1]	孟旭东, 王三华, 龚循华. 含参广义集值向量均衡问题有效解映射下半连续的最优条件[J]. 运筹学学报, 2018, 22(3): 79-88.
[2]	唐莉萍, 杨新民. 向量优化问题的一类非线性标量化定理[J]. 运筹学学报, 2016, 20(3): 85-91.
[3]	郭辉. 向量优化问题 (C,\varepsilon)-弱有效解的一种非线性标量化性质[J]. 运筹学学报, 2015, 19(2): 105-110.
[4]	夏远梅, 赵克全. 向量优化中\varepsilon-真有效解的非线性标量化性质[J]. 运筹学学报, 2014, 18(4): 58-64.