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含参集值弱向量平衡问题解集映射的半连续性 被引量：3

On the Semicontinuity of the Solution Set Map to Parametric Set-Valued Weak Vector Equilibrium Problems
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摘要 在线性度量空间中,运用标量化技巧在没有单调性与C-凹性假设下得到了含参集值弱向量平衡问题解集映射上/下半连续性的充分性条件.所得结果改进了已有文献的相应结果,并通过例子验证了所得结果. In this paper, using a scalarization technique, we provide sufficient conditions for the upper/lower semicontinuity of the solution mappings to parametric setvalued weak vector equilibrium problems without monotonicity and C-concavity in linear metric spaces. These results improve the recent ones in the literature. Some examples are given for illustration of our results.
作者 彭再云 杨新民 赵勇
机构地区 重庆交通大学理学院 内蒙古大学数学科学学院 重庆师范大学数学学院
出处 《数学学报（中文版）》 SCIE CSCD 北大核心 2013年第3期391-400,共10页 Acta Mathematica Sinica：Chinese Series
基金 国家自然科学基金(10831009 11271389 11271391) 重庆市自然科学基金(CSTC 2011BA0030 2012jjA00016) 重庆市攻关项目(CSTC 2011AC6104) 重庆市优化与系统工程重点实验室课题
关键词 含参集值弱向量平衡问题 f-有效解 上半连续性 下半连续性 标量化 parametric set-valued weak vector equilibrium problem f-efficient solu- tion upper semicontinuity lower semicontinuity scalarization
分类号 O224 [理学—运筹学与控制论]
  • 相关文献

参考文献16

  • 1Giannessi F., Vector Variational Inequalities and Vector Equilibria: Mathematical Theories, Kluwer, Dor?drecht, 2000.
  • 2Li S. J., Chen G. Y., Teo K. L., On the stability of generalized vector quasivariational inequality problems, J. Optim. Theory Appl., 2002, 113: 283-295.
  • 3Cheng Y. H., Zhu D. L., Global stability results for the weak vector variational inequality, J. Glob. Optim., 2005, 32: 543-550.
  • 4Anh L. Q., Khanh P. Q., Semicontinuity of the solution set of parametric multivalued vector quasiequilibrium problems, J. Math. Anal. Appl., 2004, 294: 699-71l.
  • 5Anh L. Q., Khanh P. Q., On the stability of the solution sets of general multivalued vector quasiequilibrium problems, J. Optim. Theory Appl., 2007, 135: 271-284.
  • 6Huang N. J., Li J., Thompson H. B., Stability for parametric implicit vector equilibrium problems, Math. Comput. Model, 2006, 43: 1267-1274.
  • 7Gong X. H., Continuity of the solution set to parametric weak vector equilibrium problems, J. Optim. Theory Appl., 2008, 139: 35-46.
  • 8Gong X. H., Yao J. C., Lower semicontinuity of the set of efficient solutions for generalized systems, J. Optim. Theory Appl., 2008, 138: 197-205.
  • 9Kimura K., Yao J. C., Sensitivity analysis of solution mappings of parametric vector quasi-equilibrium problems, J. Glob. Optim., 2008, 41: 187-202.
  • 10Xu S., Li S. J., A new proof approach to lower semicontinuity for parametric vector equilibrium problems, Optim. Lett., 2009, 3: 453-459.

同被引文献29

  • 1马先峰,廖公夫,李勇.Some Dynamical Properties in Set-valued Discrete Systems[J].Northeastern Mathematical Journal,2005,21(1):5-8. 被引量：2
  • 2Li S J, Chen G Y, Teo K L. On the stability of generalized vector quasivariational inequality problems [ J ]. J Optim Theory Appl, 2002,113:283 - 295.
  • 3Cheng Y H, Zhu D L. Global stability results for the weak vector variational inequality[ J]. J Glob Optim,2005 ,32 :543 -550.
  • 4Huang N J, Li J, Thompson H B. Stability for parametric implicit vector equilibrium problems [ J1. Math Comput Model,2006, 43 : 1267 - 1274.
  • 5Gong X H. Continuity of the solution set to parametric weak vector eqtfilibrium problems[J]. J Optim Theory Appl ,2008 ,139 :35 -46.
  • 6Chen C R, Li S J, Teo K L. Solution semicontinuity of parametric generalized vector equilibrium problems[ J]. J Glob Optim, 2009,45 : 309 - 3 1 8.
  • 7Cben C R, Li S J. On the solution continuity of parametric generalized systems [ J ]. Pacific J Optim,2010,6 : 141 - 151.
  • 8Cben B, Gong X H. Continuity of the solution set to parametric set - valued weak vector equilibrium problems [ J . Pacific J Optim,2010,6:511 - 520.
  • 9Li S ,1, Fang Z M. Louer semicontinuity d the solution mappings to a parametric generalized Ky Fan inequality[ J]. J Optim The- oy Appl,2010,147 :507 - 515.
  • 10Peng Z Y, Yang X M, Peng J W. On the lower semicontinuity of the solution mappings to parametric weak generalized Ky Fan inequality [ J ] J Optim Theory Appl,2012,152:256 - 264.

引证文献3

二级引证文献1

数学学报（中文版）
2013年 第3期

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