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Abstract and Applied Analysis
Volume 2012, Article ID 758287, 12 pages
Research Article

Global Convergence of a Spectral Conjugate Gradient Method for Unconstrained Optimization

College of Mathematics and Statistics, Chongqing Three Gorges University, Wanzhou 404000, China

Received 22 March 2012; Revised 19 June 2012; Accepted 24 June 2012

Academic Editor: Tianshou Zhou

Copyright © 2012 Jinkui Liu and Youyi Jiang. 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.


A new nonlinear spectral conjugate descent method for solving unconstrained optimization problems is proposed on the basis of the CD method and the spectral conjugate gradient method. For any line search, the new method satisfies the sufficient descent condition . Moreover, we prove that the new method is globally convergent under the strong Wolfe line search. The numerical results show that the new method is more effective for the given test problems from the CUTE test problem library (Bongartz et al., 1995) in contrast to the famous CD method, FR method, and PRP method.