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A subgradient algorithm for a class of nonlinear split feasibility problems: application to jointly constrained Nash equilibrium models

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  • Le Hai Yen

    (VAST)

  • Nguyen Thi Thanh Huyen

    (Thainguyen University of Sciences)

  • Le Dung Muu

    (VAST)

Abstract

In this paper we propose an algorithm for solving the split feasibility problem $$x\in C, Ax\in Q$$ x ∈ C , A x ∈ Q with C being the solution set of an equilibrium problem and A can be nonlinear. The proposed algorithm is a combination between the projection method for the equilibrium problem and the gradient method for the inclusion $$Ax\in Q$$ A x ∈ Q . The convergence of the algorithm is investigated. A numerical example for a jointly constrained Nash equilibrium model in electricity production market is provided to demonstrate the behavior of the algorithm.

Suggested Citation

  • Le Hai Yen & Nguyen Thi Thanh Huyen & Le Dung Muu, 2019. "A subgradient algorithm for a class of nonlinear split feasibility problems: application to jointly constrained Nash equilibrium models," Journal of Global Optimization, Springer, vol. 73(4), pages 849-868, April.
    • Handle: RePEc:spr:jglopt:v:73:y:2019:i:4:d:10.1007_s10898-018-00735-0
    DOI: 10.1007/s10898-018-00735-0
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    References listed on IDEAS

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    1. Steffan Berridge & Jacek Krawczyk, "undated". "Relaxation Algorithms in Finding Nash Equilibrium," Computing in Economics and Finance 1997 159, Society for Computational Economics.
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    4. 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.
    5. Abdellah Bnouhachem & Muhammad Noor & Mohamed Khalfaoui & Sheng Zhaohan, 2012. "On descent-projection method for solving the split feasibility problems," Journal of Global Optimization, Springer, vol. 54(3), pages 627-639, November.
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    Cited by:

    1. Qiao-Li Dong & Songnian He & Michael Th. Rassias, 2021. "General splitting methods with linearization for the split feasibility problem," Journal of Global Optimization, Springer, vol. 79(4), pages 813-836, April.

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