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A Method with Double Inertial Type and Golden Rule Line Search for Solving Variational Inequalities

Author

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  • Uzoamaka Azuka Ezeafulukwe

    (Department of Mathematics, University of Nigeria, Nsukka 410105, Nigeria)

  • Besheng George Akuchu

    (Department of Mathematics, University of Nigeria, Nsukka 410105, Nigeria)

  • Godwin Chidi Ugwunnadi

    (Department of Mathematics, University of Eswatini, Kwaluseni M201, Eswatini
    Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Medunsa, P.O. Box 94, Pretoria 0204, South Africa)

  • Maggie Aphane

    (Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Medunsa, P.O. Box 94, Pretoria 0204, South Africa)

Abstract

In this work, we study a new line-search rule for solving the pseudomonotone variational inequality problem with non-Lipschitz mapping in real Hilbert spaces as well as provide a strong convergence analysis of the sequence generated by our suggested algorithm with double inertial extrapolation steps. In order to speed up the convergence of projection and contraction methods with inertial steps for solving variational inequalities, we propose a new approach that combines double inertial extrapolation steps, the modified Mann-type projection and contraction method, and the line-search rule, which is based on the golden ratio ( 5 + 1 ) / 2 . We demonstrate the efficiency, robustness, and stability of the suggested algorithm with numerical examples.

Suggested Citation

  • Uzoamaka Azuka Ezeafulukwe & Besheng George Akuchu & Godwin Chidi Ugwunnadi & Maggie Aphane, 2024. "A Method with Double Inertial Type and Golden Rule Line Search for Solving Variational Inequalities," Mathematics, MDPI, vol. 12(14), pages 1-16, July.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:14:p:2203-:d:1434575
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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.
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