Solving unconstrained minimization problems with a new hybrid conjugate gradient method

Maulana, Malik and Mustafa, Mamat and Siti Sabariah, Abas and Ibrahim, Mohammed Sulaiman and Sukono, . and Abdul Talib, Bon (2020) Solving unconstrained minimization problems with a new hybrid conjugate gradient method. In: 5th North American International Conference on Industrial Engineering and Operations Management, 10-14 Aug 2020, Michigan, USA.

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Abstract

Conjugate gradient (CG) method is an efficient method for solving unconstrained, large-scale optimization problems. Hybridization is one of the common approaches in the 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 HajarMustafa-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 supports global convergence. The results show that the new hybrid CG has the best efficiency among the classical CG of HS, NHMR, FR, and WYL in terms of the number of iterations (NOI) and the central processing unit (CPU) per time.

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