A new trust-region method with line search for solving symmetric nonlinear equations

Abstract

A new trust-region method is proposed for symmetric nonlinear equations. In this given algorithm, if the trial step is unsuccessful, one line search will be used instead of repeatedly solving the subproblem of the normal trust-region method. Moreover, the global convergence is established under mild conditions by a new way. The quadratic convergence of the presented method is also proved. Numerical results show that the method is interesting for the given problems.

Keywords:

• trust-region method
• nonlinear equations
• line search
• global convergence
• superlinear convergence

2000 AMS Subject Classifications :

• 65K05
• 90C26

Acknowledgements

The authors would like to thank the referees and the editor for their helpful suggestions and comments which improved this paper greatly. This work is supported by China NSF grants 10761001, Guangxi SF grants 0991028, and the Scientific Research Foundation of Guangxi University (Grant No. X081082).