Iterative methods for solving variational inequalities in Euclidean space

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• 作者：Aviv Gibali ; Simeon Reich ; Rafa? Zalas
• 关键词：47H05 ; 47H09 ; 47H10 ; 47J20 ; 47J25 ; 65K15 ; Almost cyclic control ; common fixed point ; intermittent control ; iterative method ; metric projection ; nonexpansive operator ; quasinonexpansive operator ; subgradient projection ; variational inequality
• 刊名：Journal of Fixed Point Theory and Applications
• 出版年：2015
• 出版时间：December 2015
• 年：2015
• 卷：17
• 期：4
• 页码：775-811
• 全文大小：1,198 KB
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• 作者单位：Aviv Gibali (1)
  Simeon Reich (2)
  Rafa? Zalas (2)
  
  1. Department of Mathematics, ORT Braude College, 21982, Karmiel, Israel
  2. Department of Mathematics, The Technion - Israel Institute of Technology, 32000, Haifa, Israel
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  Analysis
  Mathematical Methods in Physics
  
• 出版者：Birkh盲user Basel
• ISSN：1661-7746

文摘

In this paper, we investigate the convergence properties of an iterative method for solving variational inequalities in Euclidean space. We show that under certain assumptions the method can be applied to variational inequalities defined over the common fixed point set of a given infinite family of cutter operators. The main step of our method consists in the computation of the metric projection onto a certain superhalf- space, which is constructed using the input data defining the problem. Moreover, in the case where the common fixed point set is a finite intersection of the fixed point sets of cutters for which Opial’s closedness principle holds, we show that the iterative method can be easily combined with either sequential, composition or convex combination type methods. We also discuss ways of applying our method to more general classes of operators such as quasi-nonexpansive and demi-contractive ones. Keywords Almost cyclic control common fixed point intermittent control iterative method metric projection nonexpansive operator quasinonexpansive operator subgradient projection variational inequality