Solving unconstrained minimization problems with a new hybrid conjugate gradient method

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

Research output: Contribution to journalConference articlepeer-review

1 Citation (Scopus)

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 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.

Original languageEnglish
JournalProceedings of the International Conference on Industrial Engineering and Operations Management
Issue numberAugust
Publication statusPublished - 2020
EventProceedings of the 5th NA International Conference on Industrial Engineering and Operations Management, IOEM 2020 - Virtual, United States
Duration: 10 Aug 202014 Aug 2020

Keywords

  • Conjugate gradient method
  • Exact line search
  • Global convergence
  • Hybrid conjugate gradient
  • Sufficient descent condition

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