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A Novel Method for Finding Minimum-norm Solutions to Pseudomonotone Variational Inequalities

Author

Listed:
  • Duong Viet Thong

    (Thu Dau Mot University)

  • Pham Ky Anh

    (Vietnam National University)

  • Vu Tien Dung

    (Vietnam National University)

  • Do Thi My Linh

    (Hanoi University of Industry)

Abstract

In this paper, we introduce a novel iterative method for finding the minimum-norm solution to a pseudomonotone variational inequality problem in Hilbert spaces. We establish strong convergence of the proposed method and its linear convergence under some suitable assumptions. Some numerical experiments are given to illustrate the performance of our method. Our result improves and extends some existing results in the literature.

Suggested Citation

  • Duong Viet Thong & Pham Ky Anh & Vu Tien Dung & Do Thi My Linh, 2023. "A Novel Method for Finding Minimum-norm Solutions to Pseudomonotone Variational Inequalities," Networks and Spatial Economics, Springer, vol. 23(1), pages 39-64, March.
    • Handle: RePEc:kap:netspa:v:23:y:2023:i:1:d:10.1007_s11067-022-09569-6
    DOI: 10.1007/s11067-022-09569-6
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    References listed on IDEAS

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    1. 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.
    2. 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.
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    Cited by:

    1. Austine Efut Ofem & Jacob Ashiwere Abuchu & Hossam A. Nabwey & Godwin Chidi Ugwunnadi & Ojen Kumar Narain, 2023. "On Bilevel Monotone Inclusion and Variational Inequality Problems," Mathematics, MDPI, vol. 11(22), pages 1-28, November.
    2. Pengjie Liu & Linhao Li & Hu Shao & Meixing Liu & Jiaxu Fan, 2025. "An Inertial-type CG Projection Method with Restart for Pseudo-monotone Costs with Application to Traffic Assignment," Networks and Spatial Economics, Springer, vol. 25(1), pages 147-172, March.

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