Abstract: A perturbed BFGS method was proposed in[3]to solve the unconstrained optimization and was proved to be globally convergent when the Wolfe line search is used.In this paper,we show that the perturbed BFGS method also possesses global convergence for nonconvex problems with the relatively weaker Armijo line search.Numerical results show that this method with the Armijo search is also promising. 

Key words: BGFS method, Armijo linear search , Global convergence