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Stability Property in Bifunction-Set Optimization

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  • Pham Huu Sach

    (Vietnam Academy of Science and Technology)

Abstract

This paper gives sufficient conditions for the lower and upper semicontinuities of the solution mapping of a model, called the parametric bifunction-set optimization problem, which provides a bridge between several parametric set optimization problems and parametric generalized vector Ky Fan inequality problems. Our main theorems, applied to the just mentioned problems, give some new or sharper results.

Suggested Citation

  • Pham Huu Sach, 2018. "Stability Property in Bifunction-Set Optimization," Journal of Optimization Theory and Applications, Springer, vol. 177(2), pages 376-398, May.
    • Handle: RePEc:spr:joptap:v:177:y:2018:i:2:d:10.1007_s10957-018-1280-y
    DOI: 10.1007/s10957-018-1280-y
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    4. Pham Huu Sach, 2018. "Solution Existence in Bifunction-Set Optimization," Journal of Optimization Theory and Applications, Springer, vol. 176(1), pages 1-16, January.
    5. Fioravante Patrone & Lucia Pusillo & Stef Tijs, 2007. "Multicriteria games and potentials," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 15(1), pages 138-145, July.
    6. 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.
    7. 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.
    8. Y. D. Xu & S. J. Li, 2016. "On the solution continuity of parametric set optimization problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 84(1), pages 223-237, August.
    9. Patrone, F. & Pusillo, L. & Tijs, S.H., 2007. "Multicriteria games and potentials," Other publications TiSEM 47a4248e-bbe4-4037-99f1-f, Tilburg University, School of Economics and Management.
    10. 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.
    11. 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.
    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.
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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. Pham Huu Sach & Le Anh Tuan, 2021. "Semicontinuity Property of Approximate Solution Mappings in Bifunction-Set Optimization," Journal of Optimization Theory and Applications, Springer, vol. 191(1), pages 202-228, October.

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