Abstract: In this paper, the authors present a trust region method for nonlinear system. The main idea of this paper is that by introducting slack variables, the authors transformate the problem into a nonlinear optimization with nonnegative constraints. By using active set strategy, the authors need only to solve a reduced trust region subproblem which is solved inexactly by the truncated conjugate gradient method. Under weak conditions, the authors obtain a general convergence result.

Key words: Nonlinear system, Active-set trust region method, Truncated conjugate gradient method.