The algorithms of Broyden-CG for unconstrained optimization problems - Ibrahim, Mohd Asrul Hery; Mamat, Mustafa; Leong, Wah June; Mohammad Sofi, Azfi Zaidi (Hikari, 2014)
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.