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A new algorithm for solving multi-valued variational inequality problems

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Abstract

In this paper, we present a new algorithm for solving multi-valued variational inequality problems, which combines the subgradient extragradient algorithm with inertial algorithm. We prove that the algorithm is globally convergent when the multi-valued mapping is continuous and pseudomonotone with nonempty compact convex values. And the convergence rate of this algorithm is Q-linear convergence.

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Acknowledgements

This research was supported by National Natural Science Foundations of China (11771255) and Natural Science Foundation of Shandong Province (ZR2016AM07).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Shandong University of Technology, Zibo, 255091, People’s Republic of China

    Xi Zhang, Wenling Zhao & Meng Zhang

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  1. Xi Zhang
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  2. Wenling Zhao
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  3. Meng Zhang
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Correspondence to Wenling Zhao.

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Zhang, X., Zhao, W. & Zhang, M. A new algorithm for solving multi-valued variational inequality problems. J. Appl. Math. Comput. 62, 685–699 (2020). https://doi.org/10.1007/s12190-019-01303-9

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  • DOI: https://doi.org/10.1007/s12190-019-01303-9

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