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Some New Conditions for Solving Variational Inequalities Without Monotonicity

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  • Duong Viet Thong

    (National Economics University)

Abstract

This work aims to provide some new conditions for approximating a solution of the variational inequality problem without monotonicity in a real Hilbert space. We obtain a weak convergence result of the proposed method that hasn’t been investigated before in the literature. Our results improve and extend the relaxed inertial Tseng extragradient method for the class of nonlinear mappings without using any monotonicity.

Suggested Citation

  • Duong Viet Thong, 2025. "Some New Conditions for Solving Variational Inequalities Without Monotonicity," Journal of Optimization Theory and Applications, Springer, vol. 206(2), pages 1-20, August.
    • Handle: RePEc:spr:joptap:v:206:y:2025:i:2:d:10.1007_s10957-025-02718-0
    DOI: 10.1007/s10957-025-02718-0
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    References listed on IDEAS

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    1. Chinedu Izuchukwu & Yekini Shehu & Jen-Chih Yao, 2022. "New inertial forward-backward type for variational inequalities with Quasi-monotonicity," Journal of Global Optimization, Springer, vol. 84(2), pages 441-464, October.
    2. Boţ, R.I. & Csetnek, E.R. & Vuong, P.T., 2020. "The forward–backward–forward method from continuous and discrete perspective for pseudo-monotone variational inequalities in Hilbert spaces," European Journal of Operational Research, Elsevier, vol. 287(1), pages 49-60.
    3. Rapeepan Kraikaew & Satit Saejung, 2014. "Strong Convergence of the Halpern Subgradient Extragradient Method for Solving Variational Inequalities in Hilbert Spaces," Journal of Optimization Theory and Applications, Springer, vol. 163(2), pages 399-412, November.
    4. 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.
    5. Yu. Malitsky & V. Semenov, 2015. "A hybrid method without extrapolation step for solving variational inequality problems," Journal of Global Optimization, Springer, vol. 61(1), pages 193-202, January.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
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