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Lower Semicontinuity of the Set of Efficient Solutions for Generalized Systems

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  • X. H. Gong

    (Nanchang University)

  • J. C. Yao

    (National Sun Yat-Sen University)

Abstract

We discuss the lower semicontinuity of the set of efficient solutions for parametric generalized systems with monotone bifunctions in real locally convex Hausdorff topological vector spaces.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:138:y:2008:i:2:d:10.1007_s10957-008-9379-1
    DOI: 10.1007/s10957-008-9379-1
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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. X. H. Gong & J. C. Yao, 2008. "Connectedness of the Set of Efficient Solutions for Generalized Systems," Journal of Optimization Theory and Applications, Springer, vol. 138(2), pages 189-196, August.
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    Citations

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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. 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. 150(2), pages 317-326, August.
    3. S. J. Li & Z. M. Fang, 2010. "Lower Semicontinuity of the Solution Mappings to a Parametric Generalized Ky Fan Inequality," Journal of Optimization Theory and Applications, Springer, vol. 147(3), pages 507-515, December.
    4. Adela Capătă, 2011. "Existence results for proper efficient solutions of vector equilibrium problems and applications," Journal of Global Optimization, Springer, vol. 51(4), pages 657-675, December.
    5. Pham Sach & Nguyen Minh, 2013. "Continuity of solution mappings in some parametric non-weak vector Ky Fan inequalities," Journal of Global Optimization, Springer, vol. 57(4), pages 1401-1418, December.
    6. 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.
    7. Bin Chen & Nan-jing Huang, 2013. "Continuity of the solution mapping to parametric generalized vector equilibrium problems," Journal of Global Optimization, Springer, vol. 56(4), pages 1515-1528, August.
    8. 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.
    9. Pham Huu Sach, 2018. "Stability Property in Bifunction-Set Optimization," Journal of Optimization Theory and Applications, Springer, vol. 177(2), pages 376-398, May.
    10. Ren-you Zhong & Nan-jing Huang, 2010. "Stability Analysis for Minty Mixed Variational Inequality in Reflexive Banach Spaces," Journal of Optimization Theory and Applications, Springer, vol. 147(3), pages 454-472, December.
    11. X. Gong, 2011. "Chebyshev scalarization of solutions to the vector equilibrium problems," Journal of Global Optimization, Springer, vol. 49(4), pages 607-622, April.
    12. Z. Y. Peng & X. M. Yang & J. W. Peng, 2012. "On the Lower Semicontinuity of the Solution Mappings to Parametric Weak Generalized Ky Fan Inequality," Journal of Optimization Theory and Applications, Springer, vol. 152(1), pages 256-264, January.
    13. Li, S.J. & Chen, C.R. & Li, X.B. & Teo, K.L., 2011. "Hölder continuity and upper estimates of solutions to vector quasiequilibrium problems," European Journal of Operational Research, Elsevier, vol. 210(2), pages 148-157, April.
    14. 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.

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