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Auxiliary Principle Technique for Hierarchical Equilibrium Problems

Author

Listed:
  • Pham Ngoc Anh

    (Posts and Telecommunications Institute of Technology)

  • Qamrul Hasan Ansari

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

Abstract

In this paper, building upon auxiliary principle technique and using proximal operator, we introduce a new explicit algorithm for solving monotone hierarchical equilibrium problems. The considered problem is a monotone equilibrium problem, where the constraint is the solution set of a set-valued variational inequality problem. The strong convergence of the proposed algorithm is studied under strongly monotone and Lipschitz-type assumptions of the bifunction. By combining with parallel techniques, the convergence result is also established for the equilibrium problem involving a finite system of demicontractive mappings. Several fundamental experiments are provided to illustrate the numerical behavior of the proposed algorithm and comparison with other known algorithms is studied.

Suggested Citation

  • Pham Ngoc Anh & Qamrul Hasan Ansari, 2021. "Auxiliary Principle Technique for Hierarchical Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 188(3), pages 882-912, March.
    • Handle: RePEc:spr:joptap:v:188:y:2021:i:3:d:10.1007_s10957-021-01814-1
    DOI: 10.1007/s10957-021-01814-1
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    References listed on IDEAS

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    1. P. Anh & H. Le Thi, 2013. "An Armijo-type method for pseudomonotone equilibrium problems and its applications," Journal of Global Optimization, Springer, vol. 57(3), pages 803-820, November.
    2. Monica Bianchi & Siegfried Schaible, 2004. "Equilibrium Problems under Generalized Convexity and Generalized Monotonicity," Journal of Global Optimization, Springer, vol. 30(2), pages 121-134, November.
    3. Abdellatif Moudafi, 2010. "Proximal methods for a class of bilevel monotone equilibrium problems," Journal of Global Optimization, Springer, vol. 47(2), pages 287-292, June.
    4. 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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