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Abstract and Applied Analysis
Volume 2014, Article ID 507102, 6 pages
Research Article

The Hybrid BFGS-CG Method in Solving Unconstrained Optimization Problems

1School of Applied Sciences and Foundation, Infrastructure University Kuala Lumpur, 43000 Kajang, Malaysia
2Faculty of Informatics and Computing, Universiti Sultan Zainal Abidin, Tembila Campus, 22200 Besut, Malaysia
3Department of Mathematics, Faculty of Science and Technology, Universiti Malaysia Terengganu (UMT), 21030 Kuala Terengganu, Malaysia
4Department of Mathematics, Faculty of Science, Universiti Putra Malaysia (UPM), 43400 Serdang, Malaysia

Received 22 April 2013; Accepted 23 January 2014; Published 4 March 2014

Academic Editor: Lucas Jodar

Copyright © 2014 Mohd Asrul Hery Ibrahim 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.


In solving large scale problems, the quasi-Newton method is known as the most efficient method in solving unconstrained optimization problems. Hence, a new hybrid method, known as the BFGS-CG method, has been created based on these properties, combining the search direction between conjugate gradient methods and quasi-Newton methods. In comparison to standard BFGS methods and conjugate gradient methods, the BFGS-CG method shows significant improvement in the total number of iterations and CPU time required to solve large scale unconstrained optimization problems. We also prove that the hybrid method is globally convergent.