数学物理学报(英文版)

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A NEW SELF-ADAPTIVE ITERATIVE METHOD FOR GENERAL MIXED QUASI #br# VARIATIONAL INEQUALITIES

Abdellah Bnouhachem; Mohamed Khalfaoui; Hafida Benazza   

  1. School of Management Science and Engineering, Nanjing University, Nanjing 210093, China
  • 收稿日期:2005-08-07 修回日期:2007-02-15 出版日期:2008-07-20 发布日期:2008-07-20
  • 通讯作者: Abdellah Bnouhachem
  • 基金资助:

    This research was supported by MOEC (20060284001) and by NSFC (70371019 and 10571083)

A NEW SELF-ADAPTIVE ITERATIVE METHOD FOR GENERAL MIXED QUASI #br# VARIATIONAL INEQUALITIES

Abdellah Bnouhachem; Mohamed Khalfaoui; Hafida Benazza   

  1. School of Management Science and Engineering, Nanjing University, Nanjing 210093, China
  • Received:2005-08-07 Revised:2007-02-15 Online:2008-07-20 Published:2008-07-20
  • Contact: Abdellah Bnouhachem

摘要:

The general mixed quasi variational inequality containing a nonlinear term ψ is a useful and an important generalization of variational inequalities. The projection method can not be applied to solve this problem due to the presence of nonlinear term. It is well known that the variational inequalities involving the nonlinear term ψ are equivalent to the fixed point problems and
resolvent equations. In this article, the authors use these alternative
equivalent formulations to suggest and analyze a new self-adaptive iterative method for solving general mixed quasi variational inequalities. Global convergence of the new method is proved. An example is given to illustrate the efficiency of the proposed method.

关键词: General mixed quasi variational inequalities, self-adaptive rules, resolvent operator

Abstract:

The general mixed quasi variational inequality containing a nonlinear term ψ is a useful and an important generalization of variational inequalities. The projection method can not be applied to solve this problem due to the presence of nonlinear term. It is well known that the variational inequalities involving the nonlinear term ψ are equivalent to the fixed point problems and
resolvent equations. In this article, the authors use these alternative
equivalent formulations to suggest and analyze a new self-adaptive iterative method for solving general mixed quasi variational inequalities. Global convergence of the new method is proved. An example is given to illustrate the efficiency of the proposed method.

Key words: General mixed quasi variational inequalities, self-adaptive rules, resolvent operator

中图分类号: 

  • 49J40