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Applied Mathematics and Mechanics (English Edition) ›› 2011, Vol. 2 ›› Issue (32): 241-250.doi: https://doi.org/10.1007/s10483-011-1410-8

• Articles • 上一篇    下一篇

Viscosity method for hierarchical fixed point and variational inequalities with applications

张石生1，王雄瑞1，H.W.J.LEE2，陈志坚2   

  1. 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
  • 收稿日期:2010-10-02 修回日期:2011-01-12 出版日期:2011-01-24 发布日期:2011-01-24

Viscosity method for hierarchical fixed point and variational inequalities with applications

 ZHANG Shi-Sheng1, WANG Xiong-Rui1, H.W.J.LEE2, CHEN Zhi-Jian2   

  1. 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
  • Received:2010-10-02 Revised:2011-01-12 Online:2011-01-24 Published:2011-01-24

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870

被引次数

19

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.

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.

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