Convergence property of gradient-type methods with non-monotone line search in the presence of perturbations

In this paper, two new kinds of methods which are called gradient-type method and hybrid projection method with perturbations are proposed and non-monotone line search technique is employed. At the same time, global convergence of these methods is proved only in the case where the gradient function is uniformly continuous on an open convex set containing the iteration sequence. Numerical examples are given at the end of this paper.