Comparison of conjugate gradient method on solving unconstrained optimization problems

Maulana Malik; Mustafa Mamat; Siti Sabariah Abas; Ibrahim Mohammed Sulaiman; Sukono; Abdul Talib Bon

Comparison of conjugate gradient method on solving unconstrained optimization problems

Maulana Malik
, Mustafa Mamat
, Siti Sabariah Abas
, Ibrahim Mohammed Sulaiman
, Sukono
, Abdul Talib Bon

Department of Mathematics

Research output: Contribution to journal › Conference article › peer-review

1 Citation (Scopus)

Abstract

Conjugate gradient (CG) method approaches have been instrumental in solving unconstrained optimization problems. In 2020, Malik et al. have proposed a new hybrid coefficient (H-MS2), a combination of the RMIL coefficient and the new coefficient. In this paper, we propose the new method, which takes the new coefficients from H-MS2. Also, we will compare the new method and some of the classic methods that already based on the number of iterations and central processing unit (CPU) time. The new method fulfills the sufficient descent condition and global convergence properties, and it’s tested on a set functions under exact line search. The numerical results show that the new CG method has the best efficiency between all the methods tested.

Original language	English
Journal	Proceedings of the International Conference on Industrial Engineering and Operations Management
Issue number	August
Publication status	Published - 2020
Event	Proceedings of the 5th NA International Conference on Industrial Engineering and Operations Management, IOEM 2020 - Virtual, United States Duration: 10 Aug 2020 → 14 Aug 2020

Keywords

Conjugate gradient method
Exact line search
Global convergence properties
Sufficient descent condition
Unconstrained optimization problems

Cite this

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title = "Comparison of conjugate gradient method on solving unconstrained optimization problems",

abstract = "Conjugate gradient (CG) method approaches have been instrumental in solving unconstrained optimization problems. In 2020, Malik et al. have proposed a new hybrid coefficient (H-MS2), a combination of the RMIL coefficient and the new coefficient. In this paper, we propose the new method, which takes the new coefficients from H-MS2. Also, we will compare the new method and some of the classic methods that already based on the number of iterations and central processing unit (CPU) time. The new method fulfills the sufficient descent condition and global convergence properties, and it{\textquoteright}s tested on a set functions under exact line search. The numerical results show that the new CG method has the best efficiency between all the methods tested.",

keywords = "Conjugate gradient method, Exact line search, Global convergence properties, Sufficient descent condition, Unconstrained optimization problems",

author = "Maulana Malik and Mustafa Mamat and Abas, \{Siti Sabariah\} and Sulaiman, \{Ibrahim Mohammed\} and Sukono and Bon, \{Abdul Talib\}",

note = "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: {\textcopyright} IEOM Society International. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.; Proceedings of the 5th NA International Conference on Industrial Engineering and Operations Management, IOEM 2020 ; Conference date: 10-08-2020 Through 14-08-2020",

year = "2020",

language = "English",

journal = "Proceedings of the International Conference on Industrial Engineering and Operations Management",

issn = "2169-8767",

number = "August",

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TY - JOUR

T1 - Comparison of conjugate gradient method on solving unconstrained optimization problems

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 approaches have been instrumental in solving unconstrained optimization problems. In 2020, Malik et al. have proposed a new hybrid coefficient (H-MS2), a combination of the RMIL coefficient and the new coefficient. In this paper, we propose the new method, which takes the new coefficients from H-MS2. Also, we will compare the new method and some of the classic methods that already based on the number of iterations and central processing unit (CPU) time. The new method fulfills the sufficient descent condition and global convergence properties, and it’s tested on a set functions under exact line search. The numerical results show that the new CG method has the best efficiency between all the methods tested.

AB - Conjugate gradient (CG) method approaches have been instrumental in solving unconstrained optimization problems. In 2020, Malik et al. have proposed a new hybrid coefficient (H-MS2), a combination of the RMIL coefficient and the new coefficient. In this paper, we propose the new method, which takes the new coefficients from H-MS2. Also, we will compare the new method and some of the classic methods that already based on the number of iterations and central processing unit (CPU) time. The new method fulfills the sufficient descent condition and global convergence properties, and it’s tested on a set functions under exact line search. The numerical results show that the new CG method has the best efficiency between all the methods tested.

KW - Conjugate gradient method

KW - Exact line search

KW - Global convergence properties

KW - Sufficient descent condition

KW - Unconstrained optimization problems

UR - https://www.scopus.com/pages/publications/85096531199

M3 - Conference article

AN - SCOPUS:85096531199

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 -

Comparison of conjugate gradient method on solving unconstrained optimization problems

Abstract

Keywords

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