Global Convergence of a New Nonmonotone Algorithm

In this study, we study the application of a kind of nonmonotone line search in BFGS algorithm for solving unconstrained optimization problems. This nonmonotone line search is belongs to Armijo-type line searches and when the step size is being computed at each iteration, the initial test step size can be adjusted according to the characteristics of objective functions. The global convergence of the algorithm is proved. Experiments on some well-known optimization test problems are presented to show the robustness and efficiency of the proposed algorithms.