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Mathematical Problems in Engineering
Volume 2015, Article ID 352524, 8 pages
Research Article

A New Conjugate Gradient Algorithm with Sufficient Descent Property for Unconstrained Optimization

1School of Economic Management, Xi’an University of Posts and Telecommunications, Shaanxi, Xi’an 710061, China
2School of Mathematics Science, Liaocheng University, Shandong, Liaocheng 252000, China

Received 16 May 2015; Revised 24 September 2015; Accepted 29 September 2015

Academic Editor: Masoud Hajarian

Copyright © 2015 XiaoPing Wu 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.


A new nonlinear conjugate gradient formula, which satisfies the sufficient descent condition, for solving unconstrained optimization problem is proposed. The global convergence of the algorithm is established under weak Wolfe line search. Some numerical experiments show that this new WWPNPRP+ algorithm is competitive to the SWPPRP+ algorithm, the SWPHS+ algorithm, and the WWPDYHS+ algorithm.