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On Approximating Solutions to Non-monotone Variational Inequality Problems: An Approach Through the Modified Projection and Contraction Method

Author

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  • Duong Viet Thong

    (National Economics University)

  • Vu Tien Dung

    (Department of Mathematics, Vietnam National University)

  • Pham Thi Huong Huyen

    (National Economics University)

  • Hoang Thi Thanh Tam

    (National Economics University)

Abstract

In this paper, we introduce a novel approach to approximate the solution of variational inequality problems without relying on the monotonicity assumption. We propose a two-step inertial modified projection and contraction method for solving quasi-monotone and without-monotone variational inequalities in real Hilbert spaces. We establish a weak convergence result for the proposed method under suitable conditions. Additionally, numerical examples and a network equilibrium flow problem are provided to illustrate the effectiveness of our method and compare it with recent related methods in the literature.

Suggested Citation

  • Duong Viet Thong & Vu Tien Dung & Pham Thi Huong Huyen & Hoang Thi Thanh Tam, 2024. "On Approximating Solutions to Non-monotone Variational Inequality Problems: An Approach Through the Modified Projection and Contraction Method," Networks and Spatial Economics, Springer, vol. 24(4), pages 789-818, December.
    • Handle: RePEc:kap:netspa:v:24:y:2024:i:4:d:10.1007_s11067-024-09638-y
    DOI: 10.1007/s11067-024-09638-y
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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. Xingju Cai & Guoyong Gu & Bingsheng He, 2014. "On the O(1/t) convergence rate of the projection and contraction methods for variational inequalities with Lipschitz continuous monotone operators," Computational Optimization and Applications, Springer, vol. 57(2), pages 339-363, March.
    3. Pham Ky Anh & Trinh Ngoc Hai, 2019. "Novel self-adaptive algorithms for non-Lipschitz equilibrium problems with applications," Journal of Global Optimization, Springer, vol. 73(3), pages 637-657, March.
    4. Zhong-bao Wang & Xue Chen & Jiang Yi & Zhang-you Chen, 2022. "Inertial projection and contraction algorithms with larger step sizes for solving quasimonotone variational inequalities," Journal of Global Optimization, Springer, vol. 82(3), pages 499-522, March.
    5. 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.
    6. 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.
    7. 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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