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New Scalarizing Approach to the Stability Analysis in Parametric Generalized Ky Fan Inequality Problems

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  • Pham Huu Sach

    (Hanoi Institute of Mathematics)

  • Le Anh Tuan

    (Nong Lam University
    Ninh Thuan College of Pedagogy)

Abstract

This paper gives sufficient conditions for the upper and lower semicontinuities of the solution mapping of a parametric mixed generalized Ky Fan inequality problem. We use a new scalarizing approach quite different from traditional linear scalarization approaches which, in the framework of the stability analysis of solution mappings of equilibrium problems, were useful only for weak vector equilibrium problems and only under some convexity and strict monotonicity assumptions. The main tools of our approach are provided by two generalized versions of the nonlinear scalarization function of Gerstewitz. Our stability results are new and are obtained by a unified technique. An example is given to show that our results can be applied, while some corresponding earlier results cannot.

Suggested Citation

  • Pham Huu Sach & Le Anh Tuan, 2013. "New Scalarizing Approach to the Stability Analysis in Parametric Generalized Ky Fan Inequality Problems," Journal of Optimization Theory and Applications, Springer, vol. 157(2), pages 347-364, May.
    • Handle: RePEc:spr:joptap:v:157:y:2013:i:2:d:10.1007_s10957-012-0105-7
    DOI: 10.1007/s10957-012-0105-7
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    References listed on IDEAS

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    1. 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.
    2. Lai-Jiu Lin & Qamrul Ansari & Yu-Jen Huang, 2007. "Some existence results for solutions of generalized vector quasi-equilibrium problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 65(1), pages 85-98, February.
    3. S. Li & K. Teo & X. Yang, 2005. "Generalized vector quasi-equilibrium problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 61(3), pages 385-397, July.
    4. Le Tuan & Gue Lee & Pham Sach, 2010. "Upper semicontinuity result for the solution mapping of a mixed parametric generalized vector quasiequilibrium problem with moving cones," Journal of Global Optimization, Springer, vol. 47(4), pages 639-660, August.
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    Cited by:

    1. Pham Huu Sach & Le Anh Tuan, 2022. "Existence of Solutions of Bifunction-Set Optimization Problems in Metric Spaces," Journal of Optimization Theory and Applications, Springer, vol. 192(1), pages 195-225, January.
    2. Khushboo & C. S. Lalitha, 2019. "A unified minimal solution in set optimization," Journal of Global Optimization, Springer, vol. 74(1), pages 195-211, May.
    3. 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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