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Projected solutions for finite-dimensional quasiequilibrium problems

Author

Listed:
  • Marco Castellani

    (University of L’Aquila)

  • Massimiliano Giuli

    (University of L’Aquila)

  • Sara Latini

    (University of L’Aquila)

Abstract

The concept of projected solution has been introduced in Aussel et al. (J Optim Theory Appl 170:818–837, 2016) for studying quasivariational problems where the constraint map may not be a self-map. Aim of this paper is to establish a new result on the existence of projected solutions for finite-dimensional quasiequilibrium problems without any monotonicity assumptions and without assuming the compactness of the feasible set. These two facts allow us to improve some recent results. Additionally, we deduce the existence of projected solutions for quasivariational inequalities, quasioptimization problems and generalized Nash equilibrium problems. Also, a comparison with similar results is provided.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:comgts:v:20:y:2023:i:1:d:10.1007_s10287-023-00444-4
    DOI: 10.1007/s10287-023-00444-4
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. D. Chan & J. S. Pang, 1982. "The Generalized Quasi-Variational Inequality Problem," Mathematics of Operations Research, INFORMS, vol. 7(2), pages 211-222, May.
    4. Charalambos D. Aliprantis & Kim C. Border, 2006. "Infinite Dimensional Analysis," Springer Books, Springer, edition 0, number 978-3-540-29587-7, February.
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