An improved trust region method for unconstrained optimization

In this paper, we propose an improved trust region method for solving unconstrained optimization problems. Different with traditional trust region methods, our algorithm does not resolve the subproblem within the trust region centered at the current iteration point, but within an improved one centered at some point located in the direction of the negative gradient, while the current iteration point is on the boundary set. We prove the global convergence properties of the new improved trust region algorithm and give the computational results which demonstrate the effectiveness of our algorithm.