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Viscosity method for hierarchical fixed point and variational inequalities with applications

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【Author】 Shi-sheng ZHANG1,Xiong-rui WANG1,H.W.J.LEE2,Chi-kin CHAN2(1.Department of Mathematics,Yibin University,Yibin 644007,Sichuan Province,P.R.China;2.Department of Applied Mathematics,The Hong Kong Polytechnic University,Hong Kong,P.R.China)

【机构】 Department of Mathematics,Yibin University； Department of Applied Mathematics,The Hong Kong Polytechnic University；

【摘要】 A viscosity method for a hierarchical fixed point solving variational inequality problems is presented.The method is used to solve variational inequalities,where the involved mappings are non-expansive.Solutions are sought in the set of the fixed points of another non-expansive mapping.As applications,we use the results to study problems of the monotone variational inequality,the convex programming,the hierarchical minimization,and the quadratic minimization over fixed point sets.更多还原

【Abstract】 A viscosity method for a hierarchical fixed point solving variational inequality problems is presented.The method is used to solve variational inequalities,where the involved mappings are non-expansive.Solutions are sought in the set of the fixed points of another non-expansive mapping.As applications,we use the results to study problems of the monotone variational inequality,the convex programming,the hierarchical minimization,and the quadratic minimization over fixed point sets.更多还原

【关键词】 hierarchical fixed point； non-expansive mapping； fixed point； viscosity approximation； hierarchical minimization；
【Key words】 hierarchical fixed point； non-expansive mapping； fixed point； viscosity approximation； hierarchical minimization；

【基金】 supported by the Natural Science Foundation of Yibin University (No.2009Z3)

【文献出处】 Applied Mathematics and Mechanics(English Edition) ,应用数学和力学(英文版) , 编辑部邮箱 ,2011年02期

【分类号】O177.91
【被引频次】6
【下载频次】52

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