A Two-Step Extragradient-Viscosity Method for Variational Inequalities and Fixed Point Problems
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This paper develops a two-step extragradient-viscosity method for finding a common solution to a variational inequality problem and a fixed point problem in a Hilbert space. Combining the two-step extragradient algorithm and the viscosity one, we propose a strongly convergent method, which contains as special cases some existing algorithms. Several numerical experiments are implemented to demonstrate the performance of the proposed method in comparison with classical hybrid extragradient-like algorithms.
KeywordsVariational inequality Fixed point problem Monotone operator Demicontractive mapping Extragradient method Viscosity method Hybrid method
Mathematics Subject Classification (2010)65J15 47H05 47J25 47J20 91B50
The authors would like to thank the Associate Editor and anonymous referees for their valuable comments and suggestions which help us in improving the original version of this paper.
The first-named and last-named authors are supported by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under the project: 101.01-2017.315.
- 15.Hieu, D.V.: An explicit parallel algorithm for variational inequalities. Bull. Malays. Math. Sci. Soc . https://doi.org/10.1007/s40840-017-0474-z (2017)
- 16.Hieu, D.V.: An inertial-like proximal algorithm for equilibrium problems. Math. Methods Oper Res. https://doi.org/10.1007/s00186-018-0640-6 (2018)
- 18.Hieu, D.V., Thong, D.V.: A new projection method for a class of variational inequalities. Appl. Anal. https://doi.org/10.1080/00036811.2018.1460816 (2018)
- 31.Yamada, I.: The Hybrid Steepest Descent Method for the Variational Inequality Problem over the Intersection of Fixed Point Sets of Nonexpansive Mappings. In: Inherently Parallel Algorithms for Feasibility and Optimization and Their Applications, pp. 473–504, Stud. Comput. Math 8, North-Holland, Amsterdam (2001)Google Scholar
- 35.Zykina, A.V., Meleńchuk, N.V.: A doublestep extragradient method for solving a resource management problem. Model. Anal. Inform. Sys. 17(1), 65–75 (2010)Google Scholar