Modified hybrid projection methods for finding common solutions to variational inequality problems

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• 作者：Dang Van Hieu ; Pham Ky Anh ; Le Dung Muu
• 关键词：Variational inequality ; Equilibrium problem ; Generalized equilibrium problem ; Gradient method ; Extragradient method
• 刊名：Computational Optimization and Applications
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：66
• 期：1
• 页码：75-96
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Optimization; Operations Research, Management Science; Operation Research/Decision Theory; Statistics, general; Convex and Discrete Geometry;
• 出版者：Springer US
• ISSN：1573-2894
• 卷排序：66

文摘

In this paper we propose several modified hybrid projection methods for solving common solutions to variational inequality problems involving monotone and Lipschitz continuous operators. Based on differently constructed half-spaces, the proposed methods reduce the number of projections onto feasible sets as well as the number of values of operators needed to be computed. Strong convergence theorems are established under standard assumptions imposed on the operators. An extension of the proposed algorithm to a system of generalized equilibrium problems is considered and numerical experiments are also presented.