An Improved Trust Region Method Equipped by Filter Technique

Using a filter technique, a new efficient nonmonotone trust region method is proposed. The proposed scheme is based on updating the approximation of the Hessian matrix with the scaled memoryless BFGS update formula. To update the trust region radius, an appropriate adaptive scheme is used. Moreover, a proper nonmonotone procedure is applied. Assuming some suitable assumptions, the global convergence is obtained. Numerical results are reported to show the efficiency of the offered approach.