A hybird algorithm of two kinds of trust region methods

In this paper, we propose an algorithm for nonlinear optimization problem that employs both traditional trust region methods. When solving trust region sub-problem, the traditional trust region algorithm is within the trust region centered at the current iteration point, the two improved trust region algorithms are within the trust region centered at one point located in the direction of the negative gradient ∥g_k∥. When the norm of the gradient is less than or equal to 10², we use the traditional trust region method, otherwise use the two improved trust region methods. Numerical results are given to show that the algorithm is efficient for the proposed method.