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Dynamical system for solving bilevel variational inequalities

Author

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  • Pham Ky Anh

    (Vietnam National University)

  • Trinh Ngoc Hai

    (Hanoi University of Science and Technology)

Abstract

In this paper, we propose a new algorithm for solving bilevel variational inequalities. We consider a dynamical system and prove that the trajectory of this dynamical system converges to a desired solution.

Suggested Citation

  • Pham Ky Anh & Trinh Ngoc Hai, 2021. "Dynamical system for solving bilevel variational inequalities," Journal of Global Optimization, Springer, vol. 80(4), pages 945-963, August.
    • Handle: RePEc:spr:jglopt:v:80:y:2021:i:4:d:10.1007_s10898-021-01029-8
    DOI: 10.1007/s10898-021-01029-8
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    References listed on IDEAS

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    1. Phan Tu Vuong & Jean Jacques Strodiot, 2020. "A Dynamical System for Strongly Pseudo-monotone Equilibrium Problems," Journal of Optimization Theory and Applications, Springer, vol. 185(3), pages 767-784, June.
    2. Le Quang Thuy & Trinh Ngoc Hai, 2017. "A Projected Subgradient Algorithm for Bilevel Equilibrium Problems and Applications," Journal of Optimization Theory and Applications, Springer, vol. 175(2), pages 411-431, November.
    3. M. Pappalardo & M. Passacantando, 2002. "Stability for Equilibrium Problems: From Variational Inequalities to Dynamical Systems," Journal of Optimization Theory and Applications, Springer, vol. 113(3), pages 567-582, June.
    4. J. Bello Cruz & A. Iusem, 2010. "Convergence of direct methods for paramonotone variational inequalities," Computational Optimization and Applications, Springer, vol. 46(2), pages 247-263, June.
    5. E. Cavazzuti & M. Pappalardo & M. Passacantando, 2002. "Nash Equilibria, Variational Inequalities, and Dynamical Systems," Journal of Optimization Theory and Applications, Springer, vol. 114(3), pages 491-506, September.
    6. Pham Khanh & Phan Vuong, 2014. "Modified projection method for strongly pseudomonotone variational inequalities," Journal of Global Optimization, Springer, vol. 58(2), pages 341-350, February.
    7. Dang Van Hieu & Jean Jacques Strodiot & Le Dung Muu, 2020. "An Explicit Extragradient Algorithm for Solving Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 185(2), pages 476-503, May.
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