Solving the Unconstrained Optimization Problems Using the Combination of Nonmonotone Trust Region Algorithm and Filter Technique

In this paper, we propose a new nonmonotone adaptive trust region method for solving unconstrained optimization problems that is equipped with the filter technique. In the proposed method, the various nonmonotone technique is used. Using this technique, the algorithm can advantage from nonmonotone properties and it can increase the rate of solving the problems. Also, the filter that is used in this method is the kind of finite filter. It is proofed due to the filter structure. The construction of the algorithm is based on the two interior and exterior cycles that both of them do the specified operations based on the available conditions. In the iteration of our algorithm, we use a simple subproblem for finding the trial step and we imply the corrected form of Secant condition for approximating the Hessian matrix in order to save the positive definite property of Hessian matrix. Also, the global convergence of the algorithm is established under some standard properties. Furthermore, the numerical results on some test problems show the efficiency and effectiveness of the new algorithm in comparison to some other algorithms.