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Strong convergence theorems for inertial Tseng’s extragradient method for solving variational inequality problems and fixed point problems

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Abstract

The aim of this paper is to introduce a new inertial Tseng’s extragradient algorithm for solving variational inequality problems with pseudo-monotone and Lipschitz continuous mappings and fixed point problems for nonexpansive mappings in real Hilbert spaces. We prove a strong convergence theorem for the proposed algorithm under suitable assumptions imposed on the parameters. Finally, we give some numerical experiments for supporting our main results.

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Acknowledgements

This work was supported by the NSF of China (Grant Nos. 11771063, 11971082), the Natural Science Foundation of Chongqing(cstc2020jcyj-msxmX0455), Science and Technology Project of Chongqing Education Committee (Grant No. KJZD-K201900504), the Program of Chongqing Innovation Research Group Project in University (Grant no. CXQT19018).

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Authors and Affiliations

  1. School of Mathematics Science, Chongqing Normal University, Chongqing, 401331, China

    Gang Cai

  2. College of Science, Civil Aviation University of China, Tianjin, 300300, China

    Qiao-Li Dong & Yu Peng

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  1. Gang Cai
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  2. Qiao-Li Dong
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  3. Yu Peng
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Correspondence to Gang Cai.

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Cai, G., Dong, QL. & Peng, Y. Strong convergence theorems for inertial Tseng’s extragradient method for solving variational inequality problems and fixed point problems. Optim Lett 15, 1457–1474 (2021). https://doi.org/10.1007/s11590-020-01654-4

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