含参集值弱向量平衡问题解集映射的半连续性

彭再云, 杨新民, 赵勇

数学学报 ›› 2013, Vol. 56 ›› Issue (3) : 391-400.

PDF(474 KB)
中国科学院数学与系统科学研究院期刊网
PDF(474 KB)
数学学报 ›› 2013, Vol. 56 ›› Issue (3) : 391-400. DOI: 10.12386/A2013sxxb0038
论文

含参集值弱向量平衡问题解集映射的半连续性

    彭再云1,2, 杨新民3, 赵勇3
作者信息 +

On the Semicontinuity of the Solution Set Map to Parametric Set-Valued Weak Vector Equilibrium Problems

    Zai Yun PENG1,2, Xin Min YANG3, Yong ZHAO3
Author information +
文章历史 +

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.

Abstract

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.

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

Key words

parametric set-valued weak vector equilibrium problem / f-efficient solution / upper semicontinuity / lower semicontinuity / scalarization

引用本文

EndNote

Ris (Procite)

Bibtex

导出引用
彭再云, 杨新民, 赵勇. 含参集值弱向量平衡问题解集映射的半连续性. 数学学报, 2013, 56(3): 391-400 https://doi.org/10.12386/A2013sxxb0038
Zai Yun PENG, Xin Min YANG, Yong ZHAO. On the Semicontinuity of the Solution Set Map to Parametric Set-Valued Weak Vector Equilibrium Problems. Acta Mathematica Sinica, Chinese Series, 2013, 56(3): 391-400 https://doi.org/10.12386/A2013sxxb0038

参考文献

[1] Giannessi F., Vector Variational Inequalities and Vector Equilibria: Mathematical Theories, Kluwer, Dordrecht, 2000.

[2] Li 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.

[3] Cheng Y. H., Zhu D. L., Global stability results for the weak vector variational inequality, J. Glob. Optim., 2005, 32: 543-550.

[4] Anh L. Q., Khanh P. Q., Semicontinuity of the solution set of parametric multivalued vector quasiequilibrium problems, J. Math. Anal. Appl., 2004, 294: 699-711.

[5] Anh 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.

[6] Huang N. J., Li J., Thompson H. B., Stability for parametric implicit vector equilibrium problems, Math. Comput. Model, 2006, 43: 1267-1274.

[7] Gong X. H., Continuity of the solution set to parametric weak vector equilibrium problems, J. Optim. Theory Appl., 2008, 139: 35-46.

[8] Gong X. H., Yao J. C., Lower semicontinuity of the set of efficient solutions for generalized systems, J. Optim. Theory Appl., 2008, 138: 197-205.

[9] Kimura K., Yao J. C., Sensitivity analysis of solution mappings of parametric vector quasi-equilibrium problems, J. Glob. Optim., 2008, 41: 187-202.

[10] Xu S., Li S. J., A new proof approach to lower semicontinuity for parametric vector equilibrium problems, Optim. Lett., 2009, 3: 453-459.

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

[12] Chen B., Gong X. H., Continuity of the solution set to parametric set-valued weak vector equilibrium problems, Pacific J. Optim., 2010, 6: 511-520.

[13] Li S. J., Fang Z. M., Lower semicontinuity of the solution mappings to a parametric generalized Ky Fan inequality, J. Optim. Theory Appl., 2010, 147: 507-515.

[14] Peng Z. Y., Yang X. M., Semicontinuity of the solution mappings to weak generalized parametric Ky Fan inequality problems with trifunctions, Optimization, 2012, DOI: 10.1080/02331934.2012.660693.

[15] Aubin J. P., Ekeland I., Applied Nonlinear Analysis, John Wiley & Sons, New York, 1984.

[16] Berge C., Topological Spaces, Oliver and Boyd, London, 1963.

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

PDF(474 KB)

324

Accesses

0

Citation

Detail
段落导航
相关文章

/

〈 〉