Journal of Applied Sciences1812-56541812-5662Asian Network for Scientific Information10.3923/jas.2011.1461.1464RivaieM. FauziM. MamatM. MohdI. 82011118Conjugate gradient methods play an important role in unconstrained optimization. Numerous studies and modifications have been devoted recently to improve this method. In this study a new conjugate gradient coefficient (βk) is proposed by modifying the already proven Hestenes-Steifel formula. In this new βk, a new formula for the denominator is introduced and the numerator of the original Hestenes-Steifel formula is retained. Numerical results based on the number of iterations by using exact line search have shown that this new formula of βk performs far better than the original Hestenes-Steifel, and outperforms the other conjugate gradient methods. The numerical results also suggest that this method possesses global convergence properties.]]>Al-Baali, M.,19855121124Andrei, N.,200810147161Andrei, N.,2009230570582Birgin, E.G. and J.M. Martinez,200143117128Dai, Y. and Y. Yuan,1998Dai, Y. and Y. Yuan,200010177182Dai, Y.H. and Y. Yuan,200218575582Fletcher, R. and C.M. Reeves,19647149154Gilbert, J.C. and J. Nocedal,199222142Hager, W.W and H.C. Zhang,200516170192Hestenes, M.R. and E. Steifel,195249409436Hilstrom, K.E.,19773305315Liu, Y. and C. Storey,199169129137Powell, M.J.D.,197712241254Powell, M.J.D.,1984Powell, M.J.D.,198628487500Shi, Z.J. and J. Guo,2009224444457Sun, J. and J. Zhang,2001103161173Touati-Ahmed, D. and C. Storey,199064379397Wolfe, P.,196911226235Yuan, G. and Z. Wei,2009382939Yuan, Y. and W. Sun,1999Zoutendijk, G.,19701970pp: 37-86pp: 37-86Dai, Y.H., J.Y. Han, G.H. Liu, D.F. Sun, X. Yin and Y. Yuan,199910348358