A new hybrid three-term LS-CD conjugate gradient in solving unconstrained optimization problems

The Conjugate Gradient (CG) method is renowned for its rapid convergence in optimization applications. Over the years, several modifications to CG methods have emerged to improve computational efficiency and tackle practical challenges. This paper presents a new three-term hybrid CG method for solvi...

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Main Authors: Ishak, M.A.I., Marjugi, S.M.
Format: Article
Language:English
Published: Universiti Putra Malaysia 2024
Online Access:http://psasir.upm.edu.my/id/eprint/113151/1/113151.pdf
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author Ishak, M.A.I.
Marjugi, S.M.
author_facet Ishak, M.A.I.
Marjugi, S.M.
author_sort Ishak, M.A.I.
collection UPM
description The Conjugate Gradient (CG) method is renowned for its rapid convergence in optimization applications. Over the years, several modifications to CG methods have emerged to improve computational efficiency and tackle practical challenges. This paper presents a new three-term hybrid CG method for solving unconstrained optimization problems. This algorithm utilizes a search direction that combines Liu-Storey (LS) and Conjugate Descent (CD) CG coefficients and standardizes it using a spectral which acts as a scheme for the choices of the conjugate parameters. This resultant direction closely approximates the memoryless Broyden-Fletcher-Goldfarb-Shanno (BFGS) quasi-Newton direction, known for its bounded nature and compliance with the sufficient descent condition. The paper establishes the global convergence under standard Wolfe conditions and some appropriate assumptions. Additionally, the numerical experiments were conducted to emphasize the robustness and superior efficiency of this hybrid algorithm in comparison to existing approaches.
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spelling upm.eprints-1131512024-11-18T01:31:11Z http://psasir.upm.edu.my/id/eprint/113151/ A new hybrid three-term LS-CD conjugate gradient in solving unconstrained optimization problems Ishak, M.A.I. Marjugi, S.M. The Conjugate Gradient (CG) method is renowned for its rapid convergence in optimization applications. Over the years, several modifications to CG methods have emerged to improve computational efficiency and tackle practical challenges. This paper presents a new three-term hybrid CG method for solving unconstrained optimization problems. This algorithm utilizes a search direction that combines Liu-Storey (LS) and Conjugate Descent (CD) CG coefficients and standardizes it using a spectral which acts as a scheme for the choices of the conjugate parameters. This resultant direction closely approximates the memoryless Broyden-Fletcher-Goldfarb-Shanno (BFGS) quasi-Newton direction, known for its bounded nature and compliance with the sufficient descent condition. The paper establishes the global convergence under standard Wolfe conditions and some appropriate assumptions. Additionally, the numerical experiments were conducted to emphasize the robustness and superior efficiency of this hybrid algorithm in comparison to existing approaches. Universiti Putra Malaysia 2024 Article PeerReviewed text en http://psasir.upm.edu.my/id/eprint/113151/1/113151.pdf Ishak, M.A.I. and Marjugi, S.M. (2024) A new hybrid three-term LS-CD conjugate gradient in solving unconstrained optimization problems. Malaysian Journal of Mathematical Sciences, 18 (1). pp. 167-184. ISSN 1823-8343; eISSN: 2289-750X https://mjms.upm.edu.my/lihatmakalah.php?kod=2024/March/18/1/167-184 10.47836/mjms.18.1.10
spellingShingle Ishak, M.A.I.
Marjugi, S.M.
A new hybrid three-term LS-CD conjugate gradient in solving unconstrained optimization problems
title A new hybrid three-term LS-CD conjugate gradient in solving unconstrained optimization problems
title_full A new hybrid three-term LS-CD conjugate gradient in solving unconstrained optimization problems
title_fullStr A new hybrid three-term LS-CD conjugate gradient in solving unconstrained optimization problems
title_full_unstemmed A new hybrid three-term LS-CD conjugate gradient in solving unconstrained optimization problems
title_short A new hybrid three-term LS-CD conjugate gradient in solving unconstrained optimization problems
title_sort new hybrid three term ls cd conjugate gradient in solving unconstrained optimization problems
url http://psasir.upm.edu.my/id/eprint/113151/1/113151.pdf
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