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Relaxed Two-Step Inertial Tseng’s Extragradient Method for Nonmonotone Variational Inequalities

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Listed:
  • Duong Thong

    (National Economics University)

  • Pham Anh

    (Vietnam National University)

  • Vu Dung

    (Vietnam National University)

Abstract

This work introduces a novel inertial projection method for solving the variational inequality (VI) without imposing the restrictive assumption of monotonicity on the cost operator. We establish global convergence of the proposed method under the condition that the solution set of the associated Minty VI with it is non-empty. Our results improve upon and extend many important related results in this research direction, providing a more general and flexible framework for tackling non-monotone variational inequalities. To demonstrate the practical efficacy of our method, we give some numerical illustrations and apply the proposed algorithm to solve a network equilibrium flow problem, which is a fundamental problem in transportation infrastructure modeling. We also compare the performance of our algorithm with those of existing ones.

Suggested Citation

  • Duong Thong & Pham Anh & Vu Dung, 2025. "Relaxed Two-Step Inertial Tseng’s Extragradient Method for Nonmonotone Variational Inequalities," Journal of Optimization Theory and Applications, Springer, vol. 205(1), pages 1-27, April.
    • Handle: RePEc:spr:joptap:v:205:y:2025:i:1:d:10.1007_s10957-025-02622-7
    DOI: 10.1007/s10957-025-02622-7
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    References listed on IDEAS

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    1. Yonghong Yao & Mihai Postolache, 2012. "Iterative Methods for Pseudomonotone Variational Inequalities and Fixed-Point Problems," Journal of Optimization Theory and Applications, Springer, vol. 155(1), pages 273-287, October.
    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. Timilehin O. Alakoya & Oluwatosin T. Mewomo & Yekini Shehu, 2022. "Strong convergence results for quasimonotone variational inequalities," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 95(2), pages 249-279, April.
    7. Lu-Chuan Ceng & Nicolas Hadjisavvas & Ngai-Ching Wong, 2010. "Strong convergence theorem by a hybrid extragradient-like approximation method for variational inequalities and fixed point problems," Journal of Global Optimization, Springer, vol. 46(4), pages 635-646, April.
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