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Volume 41, Issue 2
A Hybrid Conjugate Gradient Method with Trust Region for Large-Scale Unconstrained Optimization Problems

A. P. Byengonzi, P. Kaelo, M. Koorapetse & P. Mtagulwa

Ann. Appl. Math., 41 (2025), pp. 176-193.

Published online: 2025-06

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  • Abstract

In this work, we modify a conjugate gradient (CG) method recently proposed in the literature, where a PRP conjugate gradient method is modified using trust region. Particularly, we propose a hybrid CG method that incorporates the parameters $β^{PRP},$ $β^{FR}$ and $β^{CD},$ and this new search direction satisfies both the trust region feature and the sufficient descent conditions. Furthermore, under suitable conditions the developed method is proved to be globally convergent. The method is tested on some benchmark problems from the literature and numerical results show that it is quite efficient in solving large scale problems.

  • AMS Subject Headings

90C06, 90C30, 65K05

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COPYRIGHT: © Global Science Press

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@Article{AAM-41-176, author = {Byengonzi , A. P.Kaelo , P.Koorapetse , M. and Mtagulwa , P.}, title = {A Hybrid Conjugate Gradient Method with Trust Region for Large-Scale Unconstrained Optimization Problems}, journal = {Annals of Applied Mathematics}, year = {2025}, volume = {41}, number = {2}, pages = {176--193}, abstract = {

In this work, we modify a conjugate gradient (CG) method recently proposed in the literature, where a PRP conjugate gradient method is modified using trust region. Particularly, we propose a hybrid CG method that incorporates the parameters $β^{PRP},$ $β^{FR}$ and $β^{CD},$ and this new search direction satisfies both the trust region feature and the sufficient descent conditions. Furthermore, under suitable conditions the developed method is proved to be globally convergent. The method is tested on some benchmark problems from the literature and numerical results show that it is quite efficient in solving large scale problems.

}, issn = {}, doi = {https://doi.org/10.4208/aam.OA-2024-0019}, url = {http://global-sci.org/intro/article_detail/aam/24147.html} }
TY - JOUR T1 - A Hybrid Conjugate Gradient Method with Trust Region for Large-Scale Unconstrained Optimization Problems AU - Byengonzi , A. P. AU - Kaelo , P. AU - Koorapetse , M. AU - Mtagulwa , P. JO - Annals of Applied Mathematics VL - 2 SP - 176 EP - 193 PY - 2025 DA - 2025/06 SN - 41 DO - http://doi.org/10.4208/aam.OA-2024-0019 UR - https://global-sci.org/intro/article_detail/aam/24147.html KW - Conjugate gradient method, global convergence, strong Wolfe line search, trust-region. AB -

In this work, we modify a conjugate gradient (CG) method recently proposed in the literature, where a PRP conjugate gradient method is modified using trust region. Particularly, we propose a hybrid CG method that incorporates the parameters $β^{PRP},$ $β^{FR}$ and $β^{CD},$ and this new search direction satisfies both the trust region feature and the sufficient descent conditions. Furthermore, under suitable conditions the developed method is proved to be globally convergent. The method is tested on some benchmark problems from the literature and numerical results show that it is quite efficient in solving large scale problems.

Byengonzi , A. P.Kaelo , P.Koorapetse , M. and Mtagulwa , P.. (2025). A Hybrid Conjugate Gradient Method with Trust Region for Large-Scale Unconstrained Optimization Problems. Annals of Applied Mathematics. 41 (2). 176-193. doi:10.4208/aam.OA-2024-0019
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