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Two subgradient extragradient methods based on the golden ratio technique for solving variational inequality problems

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Abstract

We propose and study two new methods based on the golden ratio technique for approximating solutions to variational inequality problems in Hilbert space. The first method combines the golden ratio technique with the subgradient extragradient method. In the second method, we incorporate the alternating golden ratio technique into the subgradient extragradient method. Both methods use self-adaptive step sizes which are allowed to increase during the execution of the algorithms, thus limiting the dependence of our methods on the starting point of the scaling parameter. We prove that under appropriate conditions, the resulting methods converge either weakly or R-linearly to a solution of the variational inequality problem associated with a pseudomonotone operator. In order to show the numerical advantage of our methods, we first present the results of several pertinent numerical experiments and then compare the performance of our proposed methods with that of some existing methods which can be found in the literature.

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Acknowledgements

Both authors appreciate with thanks the efforts of the referees for their careful reading, helpful comments, and important suggestions, which have helped improve the quality of the manuscript.

Funding

Simeon Reich was partially supported by the Israel Science Foundation (grant no. 820/17), by the Fund for the Promotion of Research at the Technion (grant 2001893), and by the Technion General Research Fund (grant 2016723).

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Authors and Affiliations

  1. Department of Mathematics, The Technion – Israel Institute of Technology, 32000, Haifa, Israel

    Olawale K. Oyewole & Simeon Reich

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  1. Olawale K. Oyewole
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Both authors worked equally on the results and approved the final manuscript.

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Correspondence to Olawale K. Oyewole.

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Oyewole, O.K., Reich, S. Two subgradient extragradient methods based on the golden ratio technique for solving variational inequality problems. Numer Algor (2024). https://doi.org/10.1007/s11075-023-01746-z

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