  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.
