Abstract
The aim of this paper is to give a strong convergence theorem of a new iterative algorithm for solving variational inequalities with pseudomonotone and non-Lipschitzian operators in real Hilbert spaces. The proposed algorithm combines the inertial method and the extragradient method which simplifies and accelerates the process of convergence by establishing a new step size rule. Finally, we give some numerical experiments to show the performance of the proposed algorithm through comparison with related algorithms.
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Acknowledgements
This work was supported by the NSF of China (Grant No. 11771063, 11971082), the Natural Science Foundation of Chongqing (Grant No.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) and Fundamental Research Funds for the Central Universities (No.3122019142).
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Xie, Z., Cai, G., Li, X. et al. Strong Convergence of the Modified Inertial Extragradient Method with Line-Search Process for Solving Variational Inequality Problems in Hilbert Spaces. J Sci Comput 88, 50 (2021). https://doi.org/10.1007/s10915-021-01585-x
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DOI: https://doi.org/10.1007/s10915-021-01585-x