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Auxiliary Principle and Algorithm for Mixed Equilibrium Problems and Bilevel Mixed Equilibrium Problems in Banach Spaces

Author

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  • X. P. Ding

    (Sichuan Normal University)

Abstract

A new class of bilevel mixed equilibrium problems is introduced and studied in real Banach spaces. By using the auxiliary principle technique, new iterative algorithms for solving the mixed equilibrium problems and bilevel mixed equilibrium problems are suggested and analyzed. Strong convergence of the iterative sequences generated by the algorithms is proved under suitable conditions. The behavior of the solution set of the bilevel mixed equilibrium problem is also discussed.

Suggested Citation

  • X. P. Ding, 2010. "Auxiliary Principle and Algorithm for Mixed Equilibrium Problems and Bilevel Mixed Equilibrium Problems in Banach Spaces," Journal of Optimization Theory and Applications, Springer, vol. 146(2), pages 347-357, August.
    • Handle: RePEc:spr:joptap:v:146:y:2010:i:2:d:10.1007_s10957-010-9651-z
    DOI: 10.1007/s10957-010-9651-z
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    References listed on IDEAS

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    1. L. C. Ceng & G. Mastroeni & J. C. Yao, 2009. "Hybrid Proximal-Point Methods for Common Solutions of Equilibrium Problems and Zeros of Maximal Monotone Operators," Journal of Optimization Theory and Applications, Springer, vol. 142(3), pages 431-449, September.
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    Cited by:

    1. Ouayl Chadli & Qamrul Hasan Ansari & Suliman Al-Homidan, 2017. "Existence of Solutions and Algorithms for Bilevel Vector Equilibrium Problems: An Auxiliary Principle Technique," Journal of Optimization Theory and Applications, Springer, vol. 172(3), pages 726-758, March.
    2. X. Ding & Y. Liou & J. Yao, 2012. "Existence and algorithms for bilevel generalized mixed equilibrium problems in Banach spaces," Journal of Global Optimization, Springer, vol. 53(2), pages 331-346, June.
    3. X. P. Ding, 2012. "Auxiliary Principle and Algorithm of Solutions for a New System of Generalized Mixed Equilibrium Problems in Banach Spaces," Journal of Optimization Theory and Applications, Springer, vol. 155(3), pages 796-809, December.
    4. Khan, Suhel Ahmad & Chen, Jia-wei, 2015. "Gap function and global error bounds for generalized mixed quasi variational inequalities," Applied Mathematics and Computation, Elsevier, vol. 260(C), pages 71-81.
    5. Xie Ding, 2012. "Existence and iterative algorithm of solutions for a class of bilevel generalized mixed equilibrium problems in Banach spaces," Journal of Global Optimization, Springer, vol. 53(3), pages 525-537, July.
    6. G. Bento & J. Cruz Neto & J. Lopes & A. Soares Jr & Antoine Soubeyran, 2016. "Generalized Proximal Distances for Bilevel Equilibrium Problems," Post-Print hal-01690192, HAL.

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    1. Xie Ding, 2012. "Existence and iterative algorithm of solutions for a class of bilevel generalized mixed equilibrium problems in Banach spaces," Journal of Global Optimization, Springer, vol. 53(3), pages 525-537, July.

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