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Refinements on Gap Functions and Optimality Conditions for Vector Quasi-Equilibrium Problems via Image Space Analysis

Author

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  • Jun Li

    (China West Normal University)

  • Giandomenico Mastroeni

    (University of Pisa)

Abstract

By means of some new results on generalized systems, vector quasi-equilibrium problems with a variable ordering relation are investigated from the image perspective. Lagrangian-type optimality conditions and gap functions are obtained under mild generalized convexity assumptions on the given problem. Applications to the analysis of error bounds for the solution set of a vector quasi-equilibrium problem are also provided. These results are refinements of several authors’ works in recent years and also extend some corresponding results in the literature.

Suggested Citation

  • Jun Li & Giandomenico Mastroeni, 2018. "Refinements on Gap Functions and Optimality Conditions for Vector Quasi-Equilibrium Problems via Image Space Analysis," Journal of Optimization Theory and Applications, Springer, vol. 177(3), pages 696-716, June.
    • Handle: RePEc:spr:joptap:v:177:y:2018:i:3:d:10.1007_s10957-017-1182-4
    DOI: 10.1007/s10957-017-1182-4
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    References listed on IDEAS

    as
    1. S.-M. Guu & J. Li, 2014. "Vector quasi-equilibrium problems: separation, saddle points and error bounds for the solution set," Journal of Global Optimization, Springer, vol. 58(4), pages 751-767, April.
    2. R. I. Boţ & E. R. Csetnek & A. Moldovan, 2008. "Revisiting Some Duality Theorems via the Quasirelative Interior in Convex Optimization," Journal of Optimization Theory and Applications, Springer, vol. 139(1), pages 67-84, October.
    3. J. Li & G. Mastroeni, 2016. "Image Convexity of Generalized Systems with Infinite-Dimensional Image and Applications," Journal of Optimization Theory and Applications, Springer, vol. 169(1), pages 91-115, April.
    4. G. Mastroeni, 2012. "On the image space analysis for vector quasi-equilibrium problems with a variable ordering relation," Journal of Global Optimization, Springer, vol. 53(2), pages 203-214, June.
    5. Z. A. Zhou & X. M. Yang, 2011. "Optimality Conditions of Generalized Subconvexlike Set-Valued Optimization Problems Based on the Quasi-Relative Interior," Journal of Optimization Theory and Applications, Springer, vol. 150(2), pages 327-340, August.
    6. J. Li & N. J. Huang, 2010. "Image Space Analysis for Vector Variational Inequalities with Matrix Inequality Constraints and Applications," Journal of Optimization Theory and Applications, Springer, vol. 145(3), pages 459-477, June.
    7. G. Mastroeni & T. Rapcsák, 2000. "On Convex Generalized Systems," Journal of Optimization Theory and Applications, Springer, vol. 104(3), pages 605-627, March.
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    Cited by:

    1. Yang-Dong Xu & Cheng-Ling Zhou & Sheng-Kun Zhu, 2021. "Image Space Analysis for Set Optimization Problems with Applications," Journal of Optimization Theory and Applications, Springer, vol. 191(1), pages 311-343, October.

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