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Existence of Solutions and Algorithms for Bilevel Vector Equilibrium Problems: An Auxiliary Principle Technique

Author

Listed:
  • Ouayl Chadli

    (Ibn Zohr University)

  • Qamrul Hasan Ansari

    (Aligarh Muslim University
    King Fahd University of Petroleum and Minerals)

  • Suliman Al-Homidan

    (King Fahd University of Petroleum and Minerals)

Abstract

The main goal of this paper is to introduce and study bilevel vector equilibrium problems. We first establish some existence results for solutions of vector equilibrium problems and mixed vector equilibrium problems. We study the existence of solutions of bilevel vector equilibrium problems by considering a vector Thikhonov-type regularization procedure. By using this regularization procedure and existence results for mixed vector equilibrium problems, we establish some existence results for solutions of bilevel vector equilibrium problems. By using the auxiliary principle, we propose an algorithm for finding the approximate solutions of bilevel vector equilibrium problems. The strong convergence of the proposed algorithm is also studied.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:172:y:2017:i:3:d:10.1007_s10957-017-1062-y
    DOI: 10.1007/s10957-017-1062-y
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    References listed on IDEAS

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    Cited by:

    1. Lam Quoc Anh & Tran Quoc Duy & Le Dung Muu & Truong Van Tri, 2021. "The Tikhonov regularization for vector equilibrium problems," Computational Optimization and Applications, Springer, vol. 78(3), pages 769-792, April.
    2. Gayatri Pany & Ram N. Mohapatra & Sabyasachi Pani, 2018. "Solution of a class of equilibrium problems and variational inequalities in FC spaces," Annals of Operations Research, Springer, vol. 269(1), pages 565-582, October.

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