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Mathematical Problems in Engineering
Volume 2015, Article ID 103517, 7 pages
http://dx.doi.org/10.1155/2015/103517
Research Article

An Efficient Hybrid Conjugate Gradient Method with the Strong Wolfe-Powell Line Search

1School of Informatics and Applied Mathematics, Universiti Malaysia Terengganu, 21030 Kuala Terengganu, Terengganu, Malaysia
2Faculty of Informatics and Computing, Universiti Sultan Zainal Abidin, 21300 Kuala Terengganu, Terengganu, Malaysia
3Department of Computer Science and Mathematics, Universiti Teknologi MARA (UITM) Terengganu, Campus Kuala Terengganu, 21080 Kuala Terengganu, Terengganu, Malaysia

Received 11 March 2015; Revised 6 July 2015; Accepted 7 July 2015

Academic Editor: Haipeng Peng

Copyright © 2015 Ahmad Alhawarat 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

Conjugate gradient (CG) method is an interesting tool to solve optimization problems in many fields, such as design, economics, physics, and engineering. In this paper, we depict a new hybrid of CG method which relates to the famous Polak-Ribière-Polyak (PRP) formula. It reveals a solution for the PRP case which is not globally convergent with the strong Wolfe-Powell (SWP) line search. The new formula possesses the sufficient descent condition and the global convergent properties. In addition, we further explained about the cases where PRP method failed with SWP line search. Furthermore, we provide numerical computations for the new hybrid CG method which is almost better than other related PRP formulas in both the number of iterations and the CPU time under some standard test functions.