Explicit Extragradient-Like Method with Regularization for Variational Inequalities
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In this paper, we introduce and analyze the convergence of a new algorithm for solving a monotone and Lipschitz variational inequality problem in a Hilbert space. The algorithm uses variable stepsizes which are generated over each iteration, based on some previous iterates, and by some cheap computations. Contrary to many known algorithms, the resulting algorithm can be easily implemented without the prior knowledge of Lipschitz contant of operator, and also without any linesearch procedure. Besides, the regularization technique is suitably incorporated in the algorithm to get further convergence. Theorem of strong convergence is established under mild conditions imposed on control parameters. Some experiments are provided to illustrate the numerical behavior of the algorithm in comparison with others.
KeywordsVariational inequality monotone operator extragradient method subgradient extragradient method projection method
Mathematics Subject Classification65Y05 65K15 68W10 47H05 47H10
The authors would like to thank the Editor and the referees for their comments on the manuscript which helped in improving earlier version of this paper. The first and second authors are supported by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant No. 101.01-2017.315.
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Conflict of interest
The authors declare that they have no conflict of interest.
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