Mathematical Problems in Engineering
Volume 2010 (2010), Article ID 684705, 9 pages
Research Article

A Simple Sufficient Descent Method for Unconstrained Optimization

Institute of Applied Mathematics, College of Mathematics and Information Science, Henan University, Kaifeng 475004, China

Received 18 April 2010; Revised 26 August 2010; Accepted 26 October 2010

Academic Editor: Joaquim J. Júdice

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.


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.