Abstract
In this paper, we introduce a new iterative algorithm for solving classical variational inequalities problem with Lipschitz continuous and monotone map** in real Hilbert space. We modify the subgradient extragradient methods with a step size; an advantage of the algorithm is the computation of only one value of the map** and one projection onto the admissible set per one iteration. The convergence of the algorithm is established without the knowledge of the Lipschitz constant of the map**. Meanwhile, R-linear convergence rate is obtained under strong monotonicity assumption of the map**. Also, we generalize the method with Bregman projection. Finally, some numerical experiments are presented to show the efficiency of the proposed algorithm.
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The authors would like to thank the Associate Editor and the anonymous referees for their valuable comments and suggestions which helped to improve the original version of this paper.
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This project is supported by the Natural Science Basic Research Plan in Shaanxi Province of China (Program No. 2017JM1014).
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Yang, J., Liu, H. & Li, G. Convergence of a subgradient extragradient algorithm for solving monotone variational inequalities. Numer Algor 84, 389–405 (2020). https://doi.org/10.1007/s11075-019-00759-x
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DOI: https://doi.org/10.1007/s11075-019-00759-x