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An algorithm for quasiconvex equilibrium problems and asymptotically nonexpansive mappings: application to a Walras model with implicit supply–demand

Author

Listed:
  • Nguyen Ngoc Hai

    (Trade Union University)

  • Le Dung Muu

    (VAST)

  • Bui Dinh

    (Le Quy Don Technical University)

Abstract

We propose a normal subgradient projection algorithm for approximating a solution of equilibrium problems involving quasiconvex para-pseudomonotone bifunctions, which is also a fixed point of an asymptotically nonexpansive mapping. The proposed algorithm is a combination between a projection one for the equilibrium problem and the Ishikawa iteration scheme for the fixed point. Convergence of the algorithm is proved without any Lipschitz type condition for the bifunction. Applications to a modified Walras equilibrium model with implicit supply and demand are discussed.

Suggested Citation

  • Nguyen Ngoc Hai & Le Dung Muu & Bui Dinh, 2023. "An algorithm for quasiconvex equilibrium problems and asymptotically nonexpansive mappings: application to a Walras model with implicit supply–demand," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 98(2), pages 299-324, October.
    • Handle: RePEc:spr:mathme:v:98:y:2023:i:2:d:10.1007_s00186-023-00837-w
    DOI: 10.1007/s00186-023-00837-w
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    References listed on IDEAS

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    1. A. Tada & W. Takahashi, 2007. "Weak and Strong Convergence Theorems for a Nonexpansive Mapping and an Equilibrium Problem," Journal of Optimization Theory and Applications, Springer, vol. 133(3), pages 359-370, June.
    2. W. Takahashi & M. Toyoda, 2003. "Weak Convergence Theorems for Nonexpansive Mappings and Monotone Mappings," Journal of Optimization Theory and Applications, Springer, vol. 118(2), pages 417-428, August.
    3. Bigi, Giancarlo & Castellani, Marco & Pappalardo, Massimo & Passacantando, Mauro, 2013. "Existence and solution methods for equilibria," European Journal of Operational Research, Elsevier, vol. 227(1), pages 1-11.
    4. L. D. Muu & T. D. Quoc, 2009. "Regularization Algorithms for Solving Monotone Ky Fan Inequalities with Application to a Nash-Cournot Equilibrium Model," Journal of Optimization Theory and Applications, Springer, vol. 142(1), pages 185-204, July.
    5. Zi-Ming Wang & Yongfu Su & Sun Cho & Wandong Lou, 2011. "A new iterative algorithm for equilibrium and fixed point problems of nonexpansive mapping," Journal of Global Optimization, Springer, vol. 50(3), pages 457-472, July.
    6. Hu, Yaohua & Yang, Xiaoqi & Sim, Chee-Khian, 2015. "Inexact subgradient methods for quasi-convex optimization problems," European Journal of Operational Research, Elsevier, vol. 240(2), pages 315-327.
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