TY - JOUR
T1 - Solving unconstrained minimization problems with a new hybrid conjugate gradient method
AU - Malik, Maulana
AU - Mamat, Mustafa
AU - Abas, Siti Sabariah
AU - Sulaiman, Ibrahim Mohammed
AU - Sukono,
AU - Bon, Abdul Talib
N1 - Funding Information:
We would like to thank the reviewer for their suggestions and comments. This work is supported the Ph.D. mathematics study group on optimization field in Faculty of Informatics and Computing, Universiti Sultan Zainal Abidin (UniSZA), Terengganu, Malaysia
Publisher Copyright:
© IEOM Society International.
Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.
PY - 2020
Y1 - 2020
N2 - 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 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 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.
AB - 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 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 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.
KW - Conjugate gradient method
KW - Exact line search
KW - Global convergence
KW - Hybrid conjugate gradient
KW - Sufficient descent condition
UR - http://www.scopus.com/inward/record.url?scp=85096626496&partnerID=8YFLogxK
M3 - Conference article
AN - SCOPUS:85096626496
SN - 2169-8767
JO - Proceedings of the International Conference on Industrial Engineering and Operations Management
JF - Proceedings of the International Conference on Industrial Engineering and Operations Management
IS - August
T2 - Proceedings of the 5th NA International Conference on Industrial Engineering and Operations Management, IOEM 2020
Y2 - 10 August 2020 through 14 August 2020
ER -