Copyright © 2010 Ming-Liang Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We develop a sufficient descent method for solving large-scale unconstrained optimization problems. At each iteration, the search direction is a linear combination of the gradient at the current and the previous steps. An attractive property of this method is that the generated directions are always descent. Under some appropriate conditions, we show that the proposed method converges globally. Numerical experiments on some unconstrained minimization problems from CUTEr library are reported, which illustrate that the proposed method is promising.