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Gap Functions and Error Bounds for Generalized Mixed Vector Equilibrium Problems

Author

Listed:
  • Suhel Ahmad Khan

    (BITS-Pilani)

  • Jia-Wei Chen

    (Southwest University)

Abstract

In this paper, we consider two classes of generalized mixed vector equilibrium problems and mixed vector equilibrium problems, and propose some gap functions by using a new method, which is different from the previously known methods used in the literature. Finally, error bounds are obtained for the underlying mixed vector equilibrium problems in terms of regularized gap functions without using projection method.

Suggested Citation

  • Suhel Ahmad Khan & Jia-Wei Chen, 2015. "Gap Functions and Error Bounds for Generalized Mixed Vector Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 166(3), pages 767-776, September.
    • Handle: RePEc:spr:joptap:v:166:y:2015:i:3:d:10.1007_s10957-014-0683-7
    DOI: 10.1007/s10957-014-0683-7
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    References listed on IDEAS

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    1. K. R. Kazmi & S. A. Khan, 2009. "Existence of Solutions to a Generalized System," Journal of Optimization Theory and Applications, Springer, vol. 142(2), pages 355-361, August.
    2. L.R. Huang & K. F. Ng, 2005. "Equivalent Optimization Formulations and Error Bounds for Variational Inequality Problems," Journal of Optimization Theory and Applications, Springer, vol. 125(2), pages 299-314, May.
    3. J. Li & G. Mastroeni, 2010. "Vector Variational Inequalities Involving Set-valued Mappings via Scalarization with Applications to Error Bounds for Gap Functions," Journal of Optimization Theory and Applications, Springer, vol. 145(2), pages 355-372, May.
    4. N. J. Huang & J. Li & J. C. Yao, 2007. "Gap Functions and Existence of Solutions for a System of Vector Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 133(2), pages 201-212, May.
    5. Suhel Khan, 2011. "Generalized vector implicit quasi complementarity problems," Journal of Global Optimization, Springer, vol. 49(4), pages 695-705, April.
    6. D. Aussel & R. Correa & M. Marechal, 2011. "Gap Functions for Quasivariational Inequalities and Generalized Nash Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 151(3), pages 474-488, December.
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    Cited by:

    1. Nguyen Van Hung & Vicente Novo & Vo Minh Tam, 2022. "Error bound analysis for vector equilibrium problems with partial order provided by a polyhedral cone," Journal of Global Optimization, Springer, vol. 82(1), pages 139-159, January.
    2. Shengjie Li & Yangdong Xu & Manxue You & Shengkun Zhu, 2018. "Constrained Extremum Problems and Image Space Analysis—Part III: Generalized Systems," Journal of Optimization Theory and Applications, Springer, vol. 177(3), pages 660-678, June.

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