A new multi-step gradient method for optimization problem

Abstract

In this paper, we propose a new multi-step quasi- Newton method for solving unconstrained optimization problem. Our new gradient method is a in the frame of Barzilai and Borwein method. A multi step method is used to improve an accuracy of Hessian approximation which is in a diagonal matrix form. By incorporating a simple monotone strategy, the global convergence of our new method is achieved. Numerical results show the superiority of proposed method in compare with the BB method.