*Result*: 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 for minimizing nonconvex functions whose Hessian matrix may be singular without line search. 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. [ABSTRACT FROM AUTHOR]*