An Efficient Hybrid Conjugate Gradient Coefficient u nder Inexact Line Search

Abstract

The conjugate gradient (CG) methods are iterative procedures for unconstrained optimization problem. Many variants and alterations have been done lately to develop this method. In this research, we suggest a new hybrid CG coefficient by combining a modified Hestenes-Steifel (HS) formula with Fletcher and Reeves (FR). Theoretic proves has shown that the new technique achieves sufficient descent condition if inexact line search (strong Wolfe-Powell) is used. Besides, most of the numerical outcomes show that our technique is very efficient when compared to HS, FR and some famous hybrid CG for given standard test problems. The numerical outcomes also displayed that the new coefficient performs better than the original HS and FR methods.