Global Convergence of a Nonmonotone Trust Region Algorithm with Memory for Unconstrained Optimization

In this paper, we consider a trust region algorithm for unconstrained optimization problems. Unlike the traditional memoryless trust region methods, our trust region model includes memory of the past iteration, which makes the algorithm less myopic in the sense that its behavior is not completely dominated by the local nature of the objective function, but rather by a more global view. The global convergence is established by using a nonmonotone technique. The numerical tests are also given to show the efficiency of our proposed method.