BFGS method: a new search direction

• Main Authors: Ibrahim, Mohd Asrul Hery, Mamat, Mustafa, Leong, Wah June
• Format: Article
• Language: English
• Published: Penerbit Universiti Kebangsaan Malaysia 2014
• Online Access: http://psasir.upm.edu.my/id/eprint/36630/1/BFGS%20method.pdf; http://psasir.upm.edu.my/id/eprint/36630/; http://www.ukm.my/jsm/english_journals/vol43num10_2014/contentsVol43num10_2014.html
• Institution: Universiti Putra Malaysia

In this paper we present a new line search method known as the HBFGS method, which uses the search direction of the conjugate gradient method with the quasi-Newton updates. The Broyden-Fletcher-Goldfarb-Shanno (BFGS) update is used as approximation of the Hessian for the methods. The new algorithm is compared with the BFGS method in terms of iteration counts and CPU-time. Our numerical analysis provides strong evidence that the proposed HBFGS method is more efficient than the ordinary BFGS method. Besides, we also prove that the new algorithm is globally convergent.