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Viscosity-type inertial extragradient algorithms for solving variational inequality problems and fixed point problems

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Abstract

The paper presents two inertial viscosity-type extragradient algorithms for finding a common solution of the variational inequality problem involving a monotone and Lipschitz continuous operator and of the fixed point problem with a demicontractive mapping in real Hilbert spaces. Our algorithms use a simple step size rule which is generated by some calculations at each iteration. Two strong convergence theorems are obtained without the prior knowledge of the Lipschitz constant of the operator. The numerical behaviors of the proposed algorithms in some numerical experiments are reported and compared with previously known ones.

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Acknowledgements

The authors are very grateful to the editor and the anonymous referees for their valuable suggestions that improved the initial manuscript.

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  1. Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu, China

    Bing Tan, Zheng Zhou & Songxiao Li

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  1. Bing Tan
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  2. Zheng Zhou
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  3. Songxiao Li
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Correspondence to Songxiao Li.

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Tan, B., Zhou, Z. & Li, S. Viscosity-type inertial extragradient algorithms for solving variational inequality problems and fixed point problems. J. Appl. Math. Comput. 68, 1387–1411 (2022). https://doi.org/10.1007/s12190-021-01576-z

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