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Strong Convergence Theorems for Solving Variational Inequality Problems with Pseudo-monotone and Non-Lipschitz Operators

Author

Listed:
  • Gang Cai

    (Chongqing Normal University)

  • Qiao-Li Dong

    (Civil Aviation University of China)

  • Yu Peng

    (Civil Aviation University of China)

Abstract

In this paper, we propose a new viscosity extragradient algorithm for solving variational inequality problems of pseudo-monotone and non-Lipschitz continuous operator in real Hilbert spaces. We prove a strong convergence theorem under some appropriate conditions imposed on the parameters. Finally, we give some numerical experiments to illustrate the advantages of our proposed algorithms. The main results obtained in this paper extend and improve some related works in the literature.

Suggested Citation

  • Gang Cai & Qiao-Li Dong & Yu Peng, 2021. "Strong Convergence Theorems for Solving Variational Inequality Problems with Pseudo-monotone and Non-Lipschitz Operators," Journal of Optimization Theory and Applications, Springer, vol. 188(2), pages 447-472, February.
    • Handle: RePEc:spr:joptap:v:188:y:2021:i:2:d:10.1007_s10957-020-01792-w
    DOI: 10.1007/s10957-020-01792-w
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    References listed on IDEAS

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    1. Q. L. Dong & Y. J. Cho & L. L. Zhong & Th. M. Rassias, 2018. "Inertial projection and contraction algorithms for variational inequalities," Journal of Global Optimization, Springer, vol. 70(3), pages 687-704, March.
    2. Alfredo Iusem & Mostafa Nasri, 2011. "Korpelevich’s method for variational inequality problems in Banach spaces," Journal of Global Optimization, Springer, vol. 50(1), pages 59-76, May.
    3. 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.
    4. 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.
    5. Boţ, Radu Ioan & Csetnek, Ernö Robert & Hendrich, Christopher, 2015. "Inertial Douglas–Rachford splitting for monotone inclusion problems," Applied Mathematics and Computation, Elsevier, vol. 256(C), pages 472-487.
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    Cited by:

    1. Yanlai Song, 2021. "Hybrid Inertial Accelerated Algorithms for Solving Split Equilibrium and Fixed Point Problems," Mathematics, MDPI, vol. 9(21), pages 1-19, October.
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    3. Yun-Ling Cui & Lu-Chuan Ceng & Fang-Fei Zhang & Cong-Shan Wang & Jian-Ye Li & Hui-Ying Hu & Long He, 2022. "Modified Mann-Type Subgradient Extragradient Rules for Variational Inequalities and Common Fixed Points Implicating Countably Many Nonexpansive Operators," Mathematics, MDPI, vol. 10(11), pages 1-26, June.

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