Global convergence of a memory gradient method for unconstrained optimization

The memory gradient method is used for unconstrained optimization, especially large scale problems. The first idea of memory gradient method was proposed by Miele and Cantrell (1969) and Cragg and Levy (1969). In this paper, we present a new memory gradient method which generates a descent search direction for the objective function at every iteration. We show that our method converges globally to the solution if the Wolfe conditions are satisfied within the framework of the line search strategy. Our numerical results show that the proposed method is efficient for given standard test problems, if we choose a good parameter included in the method. Key words. unconstrained optimization, memory gradient method, descent search direction, Wolfe conditions, global convergence.