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Lipschitz Continuity of Approximate Solution Mappings to Parametric Generalized Vector Equilibrium Problems

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  • Yu Han

    (Nanchang University)

Abstract

In this paper, we establish Lipschitz continuity of strongly efficient approximate solution mapping to parametric generalized vector equilibrium problems without using monotonicity and any information of the solution mappings. Moreover, we make a new attempt to establish Lipschitz continuity of weakly efficient approximate solution mapping and efficient approximate solution mapping to parametric generalized vector equilibrium problems by using a scalarization method and a density result, respectively. As an application of the main results, we obtain Lipschitz continuity of strongly efficient approximate solution mapping, weakly efficient approximate solution mapping and efficient approximate solution mapping to parametric vector optimization problems.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:178:y:2018:i:3:d:10.1007_s10957-018-1329-y
    DOI: 10.1007/s10957-018-1329-y
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    References listed on IDEAS

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    1. 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.
    2. X. B. Li & X. J. Long & J. Zeng, 2013. "Hölder Continuity of the Solution Set of the Ky Fan Inequality," Journal of Optimization Theory and Applications, Springer, vol. 158(2), pages 397-409, August.
    3. Lam Anh & Phan Khanh, 2010. "Continuity of solution maps of parametric quasiequilibrium problems," Journal of Global Optimization, Springer, vol. 46(2), pages 247-259, February.
    4. S. J. Li & X. B. Li, 2011. "Hölder Continuity of Solutions to Parametric Weak Generalized Ky Fan Inequality," Journal of Optimization Theory and Applications, Springer, vol. 149(3), pages 540-553, June.
    5. 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.
    6. L. Q. Anh & P. Q. Khanh, 2009. "Hölder Continuity of the Unique Solution to Quasiequilibrium Problems in Metric Spaces," Journal of Optimization Theory and Applications, Springer, vol. 141(1), pages 37-54, April.
    7. Li, S.J. & Li, X.B. & Wang, L.N. & Teo, K.L., 2009. "The Hölder continuity of solutions to generalized vector equilibrium problems," European Journal of Operational Research, Elsevier, vol. 199(2), pages 334-338, December.
    8. 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.
    9. M. Bianchi & N. Hadjisavvas & S. Schaible, 1997. "Vector Equilibrium Problems with Generalized Monotone Bifunctions," Journal of Optimization Theory and Applications, Springer, vol. 92(3), pages 527-542, March.
    Full references (including those not matched with items on IDEAS)

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