Abstract

Conjugate gradient (CG) method is an efficient method for solving unconstrained, large-scale optimization problems.  Hybridization is one of the common approaches in modification of the CG method.  This paper presents a new hybrid CG and compares its efficiency with the classical CG method, which are Hestenes-Stiefel (HS), Nurul Hajar-Mustafa-Rivaie (NHMR), Fletcher-Reeves (FR) and Wei-Yao-Liu (WYL) methods.  The proposed a new hybrid CG is evaluated as a convex combination of HS and NHMR method.  Their performance is analyzed under the exact line search.  The new method satisfies the sufficient descent condition and support the global convergence.  The results show that the new hybrid CG has the best efficiency amongs the classical CG of HS, NHMR, FR and WYL in terms of number of iterations (NOI) and the central processing unit (CPU) per time.