The algorithms of Broyden-CG for unconstrained optimization problems

• Main Authors: Ibrahim, Mohd Asrul Hery, Mamat, Mustafa, Leong, Wah June, Mohammad Sofi, Azfi Zaidi
• Format: Article
• Language: English
• Published: Hikari 2014
• Online Access: http://psasir.upm.edu.my/id/eprint/5587/1/ibrahimIJMA49-52-2014.pdf; http://psasir.upm.edu.my/id/eprint/5587/; http://www.m-hikari.com/ijma/ijma-2014/ijma-49-52-2014/index.html
• Institution: Universiti Putra Malaysia

The conjugate gradient method plays an important role in solving large-scaled problems and the quasi-Newton method is known as the most efficient method in solving unconstrained optimization problems. Therefore, in this paper, the new hybrid method between the conjugate gradient method and the quasi-newton method for solving optimization problem is suggested. The Broyden family formula is used as an approximation of Hessian in the hybrid method and the quasi-Newton method. Our numerical analysis provides strong evidence that our Broyden-CG method is more efficient than the ordinary Broyden method. Furthermore, we also prove that new algorithm is globally convergent and gratify the sufficient descent condition.