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Inertial Version of Generalized Projected Reflected Gradient Method

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Abstract

This paper studies a generalized version of projected reflected gradient method coupled with inertial extrapolation step to solve variational inequalities in Hilbert spaces. Our proposed method requires one function evaluation and one projection per iteration alongside inertial extrapolation step which is motivated by the desire to devise faster and less computationally expensive iterative methods for variational inequalities. We obtain weak and linear convergence of the sequence of iterates generated by our method under some standard conditions and numerical results are given to show the efficacy of the proposed iterative scheme. Several versions of recently proposed projected reflected gradient methods in the literature are recovered from our method.

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Acknowledgements

The authors greatly appreciate the comments and suggestions of the referee and the handling editor which have improved on the earlier version of the paper.

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Authors and Affiliations

  1. Department of Mathematics, Clarkson University, Potsdam, NY, USA

    Olaniyi S. Iyiola

  2. College of Mathematics and Computer Science, Zhejiang Normal University, Jinhua, 321004, People’s Republic of China

    Yekini Shehu

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  1. Olaniyi S. Iyiola
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Correspondence to Yekini Shehu.

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Iyiola, O.S., Shehu, Y. Inertial Version of Generalized Projected Reflected Gradient Method. J Sci Comput 93, 24 (2022). https://doi.org/10.1007/s10915-022-01989-3

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