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Continuity of the solution mappings to parametric generalized strong vector equilibrium problems

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  • S. Li
  • H. Liu
  • Y. Zhang
  • Z. Fang

Abstract

In this paper, we establish the upper semicontinuity and lower semicontinuity of solution mappings to a parametric generalized strong vector equilibrium problem with setvalued mappings by using a scalarization method and a density result. The results improve the corresponding ones in the literature. Some examples are given to illustrate our results. Copyright Springer Science+Business Media New York 2013

Suggested Citation

  • S. Li & H. Liu & Y. Zhang & Z. Fang, 2013. "Continuity of the solution mappings to parametric generalized strong vector equilibrium problems," Journal of Global Optimization, Springer, vol. 55(3), pages 597-610, March.
    • Handle: RePEc:spr:jglopt:v:55:y:2013:i:3:p:597-610
    DOI: 10.1007/s10898-012-9985-1
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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. K. Kimura & J. C. Yao, 2008. "Semicontinuity of Solution Mappings of Parametric Generalized Vector Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 138(3), pages 429-443, September.
    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. Jun-Yi Fu, 2005. "Vector Equilibrium Problems. Existence Theorems and Convexity of Solution Set," Journal of Global Optimization, Springer, vol. 31(1), pages 109-119, January.
    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.
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    Cited by:

    1. Yu Han, 2018. "Lipschitz Continuity of Approximate Solution Mappings to Parametric Generalized Vector Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 178(3), pages 763-793, September.
    2. Pham Huu Sach, 2018. "Stability Property in Bifunction-Set Optimization," Journal of Optimization Theory and Applications, Springer, vol. 177(2), pages 376-398, May.

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