A new modified trust region algorithm for solving unconstrained optimization problems

Iterative methods for optimization can be classified into two categories: line search methods and trust region methods. In this paper, we propose a modified regularized Newton method without line search for minimizing nonconvex functions whose Hessian matrix may be singular. The proposed method is proved to converge globally if the Gradient and Hessian of the objective function are Lipschitz continuous. Moreover, we report numerical results that show that the proposed algorithm is competitive with the existing methods.