A modified adaptive cubic regularization method for large-scale unconstrained optimization problem

In this paper, we modify the adaptive cubic regularization method for large-scale unconstrained optimization problem by using a real positive definite scalar matrix to approximate the exact Hessian. Combining with the nonmonotone technique, we also give a variant of the modified algorithm. Under some reasonable conditions, we analyze the global convergence of the proposed methods. Numerical experiments are performed and the obtained results show satisfactory performance when compared to the standard trust region method, adaptive regularization algorithm with cubics and the simple model trust-region method.