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An extragradient algorithm for a lifted reformulation of projected solutions for quasiequilibria

Author

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  • Giancarlo Bigi

    (Università di Pisa)

  • Marco Castellani

    (Università degli Studi dell’Aquila)

  • Sara Latini

    (Università di Pisa)

Abstract

Projected solutions of a quasiequilibrium problem are shown to coincide with the (canonical) solutions of an auxiliary problem, that is obtained by doubling the variables and adding suitable penalty terms to the equilibrium bifunction. Unfortunately, the assumptions of existing algorithms for computing quasiequilibria are never met by this lifted reformulation due to its peculiar structure. Therefore, an ad-hoc version of the hyperplane extragradient algorithm is devised and its parameters are tuned appropriately to cope with the auxiliary problem. Finally, preliminary numerical results show the behaviour of the algorithm.

Suggested Citation

  • Giancarlo Bigi & Marco Castellani & Sara Latini, 2025. "An extragradient algorithm for a lifted reformulation of projected solutions for quasiequilibria," Journal of Global Optimization, Springer, vol. 92(4), pages 1071-1090, August.
    • Handle: RePEc:spr:jglopt:v:92:y:2025:i:4:d:10.1007_s10898-025-01508-2
    DOI: 10.1007/s10898-025-01508-2
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    References listed on IDEAS

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    1. Jianzhong Zhang & Biao Qu & Naihua Xiu, 2010. "Some projection-like methods for the generalized Nash equilibria," Computational Optimization and Applications, Springer, vol. 45(1), pages 89-109, January.
    2. E. L. Dias Júnior & P. J. S. Santos & A. Soubeyran & J. C. O. Souza, 2024. "On inexact versions of a quasi-equilibrium problem: a Cournot duopoly perspective," Journal of Global Optimization, Springer, vol. 89(1), pages 171-196, May.
    3. Giancarlo Bigi & Mauro Passacantando, 2016. "Gap functions for quasi-equilibria," Journal of Global Optimization, Springer, vol. 66(4), pages 791-810, December.
    4. Didier Aussel & Asrifa Sultana & Vellaichamy Vetrivel, 2016. "On the Existence of Projected Solutions of Quasi-Variational Inequalities and Generalized Nash Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 170(3), pages 818-837, September.
    5. Marco Castellani & Massimiliano Giuli & Massimo Pappalardo, 2018. "A Ky Fan Minimax Inequality for Quasiequilibria on Finite-Dimensional Spaces," Journal of Optimization Theory and Applications, Springer, vol. 179(1), pages 53-64, October.
    6. Orestes Bueno & John Cotrina, 2021. "Existence of Projected Solutions for Generalized Nash Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 191(1), pages 344-362, October.
    7. Jean Strodiot & Thi Nguyen & Van Nguyen, 2013. "A new class of hybrid extragradient algorithms for solving quasi-equilibrium problems," Journal of Global Optimization, Springer, vol. 56(2), pages 373-397, June.
    8. Marco Castellani & Massimiliano Giuli & Sara Latini, 2023. "Projected solutions for finite-dimensional quasiequilibrium problems," Computational Management Science, Springer, vol. 20(1), pages 1-14, December.
    9. John Cotrina & Javier Zúñiga, 2019. "Quasi-equilibrium problems with non-self constraint map," Journal of Global Optimization, Springer, vol. 75(1), pages 177-197, September.
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