The CG-BFGS method for unconstrained optimization problems

• Main Authors: Ibrahim, Mohd Asrul Hery, Mamat, Mustafa, Leong, Wah June, Mohammad Sofi, Azfi Zaidi
• Format: Conference or Workshop Item
• Language: English
• Published: AIP Publishing LLC 2013
• Online Access: http://psasir.upm.edu.my/id/eprint/36856/1/The%20CG-BFGS%20method%20for%20unconstrained%20optimization%20problems.pdf; http://psasir.upm.edu.my/id/eprint/36856/

In this paper we present a new search direction known as the CG-BFGS method, which uses the search direction of the conjugate gradient method approach in the quasi-Newton methods. The new algorithm is compared with the quasi-Newton methods in terms of the number of iterations and CPU-time. The Broyden-Fletcher-Goldfarb-Shanno (BFGS) method is used as an updating formula for the approximation of the Hessian for both methods. Our numerical analysis provides strong evidence that our CG-BFGS method is more efficient than the ordinary BFGS method. Besides, we also prove that the new algorithm is globally convergent.