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Accelerated Subgradient Extragradient Methods for Variational Inequality Problems

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Abstract

In this paper, we introduce two new iterative algorithms for solving monotone variational inequality problems in real Hilbert spaces, which are based on the inertial subgradient extragradient algorithm, the viscosity approximation method and the Mann type method, and prove some strong convergence theorems for the proposed algorithms under suitable conditions. The main results in this paper improve and extend some recent works given by some authors. Finally, the performances and comparisons with some existing methods are presented through several preliminary numerical experiments.

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Acknowledgements

The second named author is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant No. 101.01-2017.08.

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Correspondence to Duong Viet Thong.

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Dedicated to Professor Pham Ky Anh on the Occasion of his 70th Birthday.

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Thong, D.V., Vinh, N.T. & Cho, Y.J. Accelerated Subgradient Extragradient Methods for Variational Inequality Problems. J Sci Comput 80, 1438–1462 (2019). https://doi.org/10.1007/s10915-019-00984-5

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