Effective nonmonotone trust region method based on a simple cubic model for unconstrained optimization problems

In this study, we introduce a new nonmonotone trust region method with a simple cubic model to solve the unconstrained optimization problems (UCM). We improved the adaptive cubic regularization method by using a real positive definite scalar matrix instead of the exact Hessian and combining it with the nonmonotone technique. In addition, under some proper assumptions, the global convergence of the introduced method is established. Numerical tests on a set of standard minimization problems are reported and show that the proposed algorithm is efficient and robust compared to the other given methods.