A Class of Nonmontone Line Search Method with Perturbations

In this paper, a new kind of nonmontone line search method which is called new hybrid projection method with perturbations is proposed. At the same time, global convergence of this kind of method is proved only in the case where the gradient function is uniformly continuous on an open convex set containing the iteration sequence. In doing so, we remove various boundedness conditions. Furthermore, we obtain that the convergence property of gradient-type method with new nonmontone linear search method will not be changed when search directions are perturbed slightly. Numerical examples are given in the third section of this paper.