Hostname: page-component-78c5997874-ndw9j Total loading time: 0 Render date: 2024-11-10T19:41:37.670Z Has data issue: false hasContentIssue false
  • English
  • Français

LOWER SEMICONTINUITY OF PARAMETRIC GENERALIZED WEAK VECTOR EQUILIBRIUM PROBLEMS

Part of: Optimality conditions

Published online by Cambridge University Press:  02 October 2009

SHENG-JIE LI ,
HUI-MIN LIU  and
CHUN-RONG CHEN
SHENG-JIE LI
Affiliation:
College of Mathematics and Science, Chongqing University, Chongqing, 400030, PR China (email: lisj@cqu.edu.cn)
HUI-MIN LIU
Affiliation:
College of Mathematics and Science, Chongqing University, Chongqing, 400030, PR China (email: lhmmath@163.com)
CHUN-RONG CHEN*
Affiliation:
College of Mathematics and Science, Chongqing University, Chongqing, 400030, PR China (email: chencr1981@163.com)
*
✉For correspondence; e-mail: chencr1981@163.com
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper, using a scalarization method, we obtain sufficient conditions for the lower semicontinuity and continuity of the solution mapping to a parametric generalized weak vector equilibrium problem with set-valued mappings.

Keywords

lower semicontinuitysolution mappingsparametric generalized weak vector equilibrium problemsscalarization

MSC classification

Secondary: 49K40: Sensitivity, stability, well-posedness
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 81 , Issue 1 , February 2010 , pp. 85 - 95
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2009

Footnotes

This research was partially supported by the National Natural Science Foundation of China (Grant number: 10871216).

References

[1]Anh, L. Q. and Khanh, P. Q., ‘Semicontinuity of the solution set of parametric multivalued vector quasiequilibrium problems’, J. Math. Anal. Appl. 294 (2004), 699–711.Google Scholar
[2]Anh, L. Q. and Khanh, P. Q., ‘On the stability of the solution sets of general multivalued vector quasiequilibrium problems’, J. Optim. Theory Appl. 135 (2007), 271–284.Google Scholar
[3]Aubin, J. P. and Ekeland, I., Applied Nonlinear Analysis (John Wiley and Sons, New York, 1984).Google Scholar
[4]Berge, C., Topological Spaces (Oliver and Boyd, London, 1963).Google Scholar
[5]Chen, G. Y., Huang, X. X. and Yang, X. Q., Vector Optimization: Set-valued and Variational Analysis (Springer, Berlin, 2005).Google Scholar
[6]Chen, C. R. and Li, S. J., ‘Semicontinuity of the solution set map to a set-valued weak vector variational inequality’, J. Ind. Manag. Optim. 3 (2007), 519–528.CrossRefGoogle Scholar
[7]Chen, C. R., Li, S. J. and Teo, K. L., ‘Solution semicontinuity of parametric generalized vector equilibrium problems’, J. Global Optim. 45 (2009), 309–318.CrossRefGoogle Scholar
[8]Cheng, Y. H. and Zhu, D. L., ‘Global stability results for the weak vector variational inequality’, J. Global Optim. 32 (2005), 543–550.Google Scholar
[9]Ferro, F., ‘A minimax theorem for vector-valued functions’, J. Optim. Theory Appl. 60 (1989), 19–31.Google Scholar
[10]Giannessi (ed.), F., Vector Variational Inequalities and Vector Equilibria: Mathematical Theories (Kluwer, Dordrecht, 2000).CrossRefGoogle Scholar
[11]Gong, X. H., ‘Continuity of the solution set to parametric weak vector equilibrium problems’, J. Optim. Theory Appl. 139 (2008), 35–46.Google Scholar
[12]Gong, X. H. and Yao, J. C., ‘Lower semicontinuity of the set of efficient solutions for generalized systems’, J. Optim. Theory Appl. 138 (2008), 197–205.CrossRefGoogle Scholar
[13]Huang, N. J., Li, J. and Thompson, H. B., ‘Stability for parametric implicit vector equilibrium problems’, Math. Comput. Modelling 43 (2006), 1267–1274.Google Scholar
[14]Jahn, J., Vector Optimization—Theory, Applications and Extensions (Springer, Berlin, 2004).Google Scholar
[15]Khanh, P. Q. and Luu, L. M., ‘Upper semicontinuity of the solution set to parametric vector quasivariational inequalities’, J. Global Optim. 32 (2005), 569–580.Google Scholar
[16]Kimura, K. and Yao, J. C., ‘Semicontinuity of solution mappings of parametric generalized vector equilibrium problems’, J. Optim. Theory Appl. 138 (2008), 429–443.Google Scholar
[17]Kimura, K. and Yao, J. C., ‘Sensitivity analysis of solution mappings of parametric vector quasi-equilibrium problems’, J. Global Optim. 41 (2008), 187–202.Google Scholar
[18]Li, S. J. and Chen, C. R., ‘Stability of weak vector variational inequality’, Nonlinear Anal. 70 (2009), 1528–1535.CrossRefGoogle Scholar
[19]Li, S. J., Chen, G. Y. and Teo, K. L., ‘On the stability of generalized vector quasivariational inequality problems’, J. Optim. Theory Appl. 113 (2002), 283–295.CrossRefGoogle Scholar
[20]Li, S. J. and Fang, Z. M., ‘On the stability of a dual weak vector variational inequality problem’, J. Ind. Manag. Optim. 4 (2008), 155–165.Google Scholar
[21]Li, J. and Huang, N. J., ‘Implicit vector equilibrium problems via nonlinear scalarization’, Bull. Austral. Math. Soc. 72 (2005), 161–172.Google Scholar
[22]Song, W., ‘Vector equilibrium problems with set-valued mappings’, in: Vector Variational Inequalities and Vector Equilibria: Mathematical Theories (ed. Giannessi, F.) (Kluwer, Dordrecht, 2000), pp. 403–422.CrossRefGoogle Scholar