Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 910303, 9 pages
http://dx.doi.org/10.1155/2012/910303
Research Article

Global Convergence of a Modified LS Method

Liu JinKui and Du Xianglin

School of Mathematics and Statistics, Chongqing Three Gorges University, Chongqing 404000, China

Received 14 October 2011; Revised 20 December 2011; Accepted 5 January 2012

Academic Editor: Xing-Gang Yan

Copyright © 2012 Liu JinKui and Du Xianglin. 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

The LS method is one of the effective conjugate gradient methods in solving the unconstrained optimization problems. The paper presents a modified LS method on the basis of the famous LS method and proves the strong global convergence for the uniformly convex functions and the global convergence for general functions under the strong Wolfe line search. The numerical experiments show that the modified LS method is very effective in practice.