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Lower Semicontinuity for Parametric Weak Vector Variational Inequalities in Reflexive Banach Spaces

Author

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  • Ren-you Zhong

    (Sichuan University)

  • Nan-jing Huang

    (Sichuan University)

Abstract

In this paper, we study the solution stability of parametric weak Vector Variational Inequalities with set-valued and single-valued mappings, respectively. We obtain the lower semicontinuity of the solution mapping for the parametric set-valued weak Vector Variational Inequality with strictly C-pseudomapping in reflexive Banach spaces. Moreover, under some requirements that the mapping satisfies the degree conditions, we establish the lower semicontinuity of the solution mapping for a parametric single-valued weak Vector Variational Inequality in reflexive Banach spaces, by using the degree-theoretic approach. The results presented in this paper improve and extend some known results due to Kien and Yao (Set-Valued Anal. 16:399–412, 2008) and Wong (J. Glob. Optim. 46:435–446, 2010).

Suggested Citation

  • Ren-you Zhong & Nan-jing Huang, 2011. "Lower Semicontinuity for Parametric Weak Vector Variational Inequalities in Reflexive Banach Spaces," Journal of Optimization Theory and Applications, Springer, vol. 149(3), pages 564-579, June.
    • Handle: RePEc:spr:joptap:v:149:y:2011:i:3:d:10.1007_s10957-011-9805-7
    DOI: 10.1007/s10957-011-9805-7
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    References listed on IDEAS

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    1. S.J. Li & G.Y. Chen & K.L. Teo, 2002. "On the Stability of Generalized Vector Quasivariational Inequality Problems," Journal of Optimization Theory and Applications, Springer, vol. 113(2), pages 283-295, May.
    2. L. Q. Anh & P. Q. Khanh, 2007. "On the Stability of the Solution Sets of General Multivalued Vector Quasiequilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 135(2), pages 271-284, November.
    3. X. H. Gong & J. C. Yao, 2008. "Lower Semicontinuity of the Set of Efficient Solutions for Generalized Systems," Journal of Optimization Theory and Applications, Springer, vol. 138(2), pages 197-205, August.
    4. Mu Wong, 2010. "Lower semicontinuity of the solution map to a parametric vector variational inequality," Journal of Global Optimization, Springer, vol. 46(3), pages 435-446, March.
    5. X. H. Gong, 2008. "Continuity of the Solution Set to Parametric Weak Vector Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 139(1), pages 35-46, October.
    6. Stella Dafermos, 1988. "Sensitivity Analysis in Variational Inequalities," Mathematics of Operations Research, INFORMS, vol. 13(3), pages 421-434, August.
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    Cited by:

    1. C. R. Chen & S. J. Li, 2013. "Semicontinuity Results on Parametric Vector Variational Inequalities with Polyhedral Constraint Sets," Journal of Optimization Theory and Applications, Springer, vol. 158(1), pages 97-108, July.

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