A trust-region-based BFGS method with line search technique for symmetric nonlinear equations

A trust-region-based BFGS (Broyden–Fletcher–Goldfarb–Shanno) method is proposed for solving symmetric nonlinear equations. In this given algorithm, if the trial step is unsuccessful, the line search technique will be used instead of repeatedly solving the subproblem of the normal trust-region method. We establish the global and superlinear convergence of the method under suitable conditions. Numerical results show that the given method is competitive to the normal trust region method.