Developments in computational optimization techniques of conjugate gradient coefficient, search direction, Broyden-Fletcher-Goldfarb-Shanno, symmetric-rank one and Davidon-Fletcher-Powell quasi-Newton methods

Abstract

In this paper, we propose a modified Conjugate Gradient Coefficient (𝛽) for solving unconstrained minimization problems as well as the Broyden-Fletcher-Goldfarb-Shanno, Davidon-Fletcher-Powell (DFP) and Symmetric-Rank-One (SR1) updates. The modified. It is proved that the resulting Conjugate Gradient Coefficient have global convergence under some mild conditions as well as the search direction(𝑑). It is also proved that the search direction plays a key role in the line search method and the step size approaches mainly guarantee global convergence in general cases. The convergence rate of this method is also investigated. Some numerical results show that the modified Conjugate Gradient Coefficient algorithm is effective in practical computation.