Convergence property of a class of unconstrained minimization methods with perturbations

In this paper, we investigate a class of unconstrained minimization methods including Fletcher-Reeves (abbr. FR) conjugate gradient method with perturbations. Their stepsizes are determined by generalized Wolfe line search. We prove that these methods are globally convergent under mild conditions, and in doing so, we remove various boundedness conditions such as boundedness from blow of f, boundedness of level set, etc. At the end of this paper, numerical examples are given.