Using a trust region method with nonmonotone technique to solve unrestricted optimization problem

Abstract

In this work, we combine adaptive trust region method TRM with nonmonotone strategy to introduce a new algorithm to solve systems of unconstrained optimization problems depending on the simple quadratic model. The subproblems will be solving easier with the new approximation of the Hessian function. This technique does not need large capacity and is characterized by ease of application. We established the algorithm convergence with standard assumptions. The numerical results compered the performance of the new approach with three famous algorithms in terms of the time consumed to find the solution in addition to the number of iterations and the number of functions evaluations. From these results we can show that the new method is the best among the traditional algorithms.