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Extrapolated sequential constraint method for variational inequality over the intersection of fixed-point sets

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Abstract

This paper deals with the solving of variational inequality problem where the constrained set is given as the intersection of a number of fixed-point sets. To this end, we present an extrapolated sequential constraint method. At each iteration, the proposed method is updated based on the ideas of a hybrid conjugate gradient method used to accelerate the well-known hybrid steepest descent method, and an extrapolated cyclic cutter method for solving a common fixed-point problem. We prove strong convergence of the method under some suitable assumptions of step-size sequences. We finally show the numerical efficiency of the proposed method compared to some existing methods.

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Acknowledgements

The authors are thankful to the Editor and two anonymous referees for comments and remarks which improved the quality and presentation of the paper. Mootta Prangprakhon was partially supported by Science Achievement Scholarship of Thailand (SAST), and Faculty of Science, Khon Kaen University. Nimit Nimana was partially supported by Thailand Science Research and Innovation under the project IRN62W0007.

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  1. Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen, 40002, Thailand

    Mootta Prangprakhon & Nimit Nimana

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  1. Mootta Prangprakhon
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  2. Nimit Nimana
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Correspondence to Nimit Nimana.

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Prangprakhon, M., Nimana, N. Extrapolated sequential constraint method for variational inequality over the intersection of fixed-point sets. Numer Algor 88, 1051–1075 (2021). https://doi.org/10.1007/s11075-021-01067-z

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