An Efficient Modified Hestenes-Steifel Conjugate Gradient Method with Global Convergence Properties Under Strong Wolfe Powell Line Search for Largeâ€“Scale Unconstrained Optimization - Alkhouli, Talat; Mamat, Mustafa; Rivaie, Mohd; ., Sukono; Afendee Mohamed, Mohamad; Liza Ghazali, Puspa (International Journal of Engineering and Technology, 2018)
Conjugate gradient method has been widely used for solving unconstrained optimization and famously known for its low memory requirements and global convergence properties. Many works have been directed towards improving this method. In this paper, we propose a superior conjugate gradient coefficient 14Ø®Â²k"> Â by revising the already proven Hestenes-Steifel formula. Theoretical proofs show that the new method fulfils sufficient descent condition if strong Wolfe-Powell inexact line search is used. Moreover, the numerical results showed that the proposed method has outclassed the exiting CG coefficients operating under standard test set. The numerical results also showed that the new formula for 14Ø®Â²k"> Â performs significantly better than that of the original Hestenes-Steifel.Â Â