A new trust region method for nonlinear equations

In this paper, a new trust region method for the system of nonlinear equations is presented in which the determining of the trust region radius incorporates the information of its natural residual. The global convergence is obtained under mild conditions. Unlike traditional trust region method, the superlinear convergence of the method is proven under the local error bound condition. This condition is weaker than the nondegeneracy assumption which is necessary for superlinear convergence of traditional trust region method. We also propose an approximate algorithm for the trust region subproblem. Preliminary numerical experiments are reported. Acknowledgements.The authors are indebted to our supervisor, Professor Y.-X. Yuan, for his excellent guidance and Jorge J. Moré for his subroutine. And we would like to thank the referees for their valuable suggestions and comments.