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A Self Adaptive Projected Gradient Method for Solving Non-Monotone Variational Inequalities

Author

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  • Duong Viet Thong

    (National Economics University)

  • Vu Tien Dung

    (Vietnam National University)

  • Hoang Thi Thanh Tam

    (National Economics University)

Abstract

In this paper, we introduce a new modified golden ratio algorithm with adaptive stepsize rules for solving non-monotone variational inequalities in infinite-dimensional Hilbert spaces. The weak convergence and convergence rate of the proposed algorithm are established under some standard conditions. Finally, to demonstrate the practical efficacy of our method, we give some numerical illustrations and we apply the proposed algorithm to solve a network equilibrium flow problem, which is a fundamental problem in transportation infrastructure modeling. Additionally, we compare the performance of our algorithm with other existing methods.

Suggested Citation

  • Duong Viet Thong & Vu Tien Dung & Hoang Thi Thanh Tam, 2025. "A Self Adaptive Projected Gradient Method for Solving Non-Monotone Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 206(1), pages 1-27, July.
    • Handle: RePEc:spr:joptap:v:206:y:2025:i:1:d:10.1007_s10957-025-02674-9
    DOI: 10.1007/s10957-025-02674-9
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    References listed on IDEAS

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    1. Jun Yang & Hongwei Liu, 2020. "A self-adaptive method for pseudomonotone equilibrium problems and variational inequalities," Computational Optimization and Applications, Springer, vol. 75(2), pages 423-440, March.
    2. Y. Censor & A. Gibali & S. Reich, 2011. "The Subgradient Extragradient Method for Solving Variational Inequalities in Hilbert Space," Journal of Optimization Theory and Applications, Springer, vol. 148(2), pages 318-335, February.
    3. Minglu Ye & Yiran He, 2015. "A double projection method for solving variational inequalities without monotonicity," Computational Optimization and Applications, Springer, vol. 60(1), pages 141-150, January.
    4. Jun Yang & Hongwei Liu, 2018. "A Modified Projected Gradient Method for Monotone Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 179(1), pages 197-211, October.
    5. Hongwei Liu & Jun Yang, 2020. "Weak convergence of iterative methods for solving quasimonotone variational inequalities," Computational Optimization and Applications, Springer, vol. 77(2), pages 491-508, November.
    6. Hoai, Pham Thi, 2025. "A new proximal gradient method for solving mixed variational inequality problems with a novel explicit stepsize and applications," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 229(C), pages 594-610.
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