A sufficient descent hybrid conjugate gradient method without line search consideration and application
ISSN: 0264-4401
Article publication date: 18 June 2024
Issue publication date: 9 July 2024
Abstract
Purpose
Previous RMIL versions of the conjugate gradient method proposed in literature exhibit sufficient descent with Wolfe line search conditions, yet their global convergence depends on certain restrictions. To alleviate these assumptions, a hybrid conjugate gradient method is proposed based on the conjugacy condition.
Design/methodology/approach
The conjugate gradient (CG) method strategically alternates between RMIL and KMD CG methods by using a convex combination of the two schemes, mitigating their respective weaknesses. The theoretical analysis of the hybrid method, conducted without line search consideration, demonstrates its sufficient descent property. This theoretical understanding of sufficient descent enables the removal of restrictions previously imposed on versions of the RMIL CG method for global convergence result.
Findings
Numerical experiments conducted using a hybrid strategy that combines the RMIL and KMD CG methods demonstrate superior performance compared to each method used individually and even outperform some recent versions of the RMIL method. Furthermore, when applied to solve an image reconstruction model, the method exhibits reliable results.
Originality/value
The strategy used to demonstrate the sufficient descent property and convergence result of RMIL CG without line search consideration through hybrid techniques has not been previously explored in literature. Additionally, the two CG schemes involved in the combination exhibit similar sufficient descent structures based on the assumption regarding the norm of the search direction.
Keywords
Acknowledgements
2020 Mathematics Subject Classification: 65K05, 90C06, 90C30, 90C47, 90C90
The authors acknowledge the support provided by the Petchra Pra Jom Klao PhD Scholarship of King Mongkut’s University of Technology Thonburi (KMUTT) with Contract No. 52/2564 and Center of Excellence in Theoretical and Computational Science (TaCS-CoE), KMUTT.
Citation
Salihu, N., Kumam, P., Ibrahim, S.M. and Babando, H.A. (2024), "A sufficient descent hybrid conjugate gradient method without line search consideration and application", Engineering Computations, Vol. 41 No. 5, pp. 1203-1232. https://doi.org/10.1108/EC-12-2023-0912
Publisher
:Emerald Publishing Limited
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