Two modified PRP conjugate gradient methods and their global convergence for unconstrained optimization

Sun, Zhiyong; Xue, Cong; Guo, Yingying; Yuncheng, Ge; Sun, Yingwei

doi:10.1109/ccdc.2017.7978627

Cited by 3 publications

(2 citation statements)

References 14 publications

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“…The second category which includes: Fletcher and Revees (FR) (Fletcher and Reeves, 1964), Dai and Yuan (DY) (Dai and Yuan, 1999), and Conjugate Descent (CD) (Fletcher, 1987) possess strong convergence properties but their numerical performance is affected by jamming phenomena (Liu and Li, 2014). These shortcomings prompted some modifications of the CG formulas (see: (Aminifard and Babaie-Kafaki, 2019; Ibrahim and Mustafa, 2020; Liu and Feng, 2019; Rivaie et al ., 2012; Zhang et al ., 2006; Zhongbo et al ., 2017)). Much efforts have been made in finding better modifications of the CG formulas which not only produce sufficient descent direction and efficient computational performance, but also satisfy some conjugacy conditions (Awwal et al ., 2023).…”

Section: Introductionmentioning

confidence: 99%

A sufficient descent hybrid conjugate gradient method without line search consideration and application

Salihu,

Kumam,

Ibrahim

et al. 2024

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PurposePrevious 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/approachThe 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.FindingsNumerical 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/valueThe 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.

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Section: Introductionmentioning

confidence: 99%

A sufficient descent hybrid conjugate gradient method without line search consideration and application

Salihu,

Kumam,

Ibrahim

et al. 2024

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“…Unfortunately, their numerical results are not promising even with inexact line minimization. The following references are available for more information on hybrid and spectral CG methods [27,[38][39][40][41][42][43][44][45][46][47].…”

Section: Introductionmentioning

confidence: 99%

The global convergence of spectral RMIL conjugate gradient method for unconstrained optimization with applications to robotic model and image recovery

Salihu

Awwal²,

Sulaiman³

et al. 2023

PLoS ONE

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In 2012, Rivaie et al. introduced RMIL conjugate gradient (CG) method which is globally convergent under the exact line search. Later, Dai (2016) pointed out abnormality in the convergence result and thus, imposed certain restricted RMIL CG parameter as a remedy. In this paper, we suggest an efficient RMIL spectral CG method. The remarkable feature of this method is that, the convergence result is free from additional condition usually imposed on RMIL. Subsequently, the search direction is sufficiently descent independent of any line search technique. Thus, numerical experiments on some set of benchmark problems indicate that the method is promising and efficient. Furthermore, the efficiency of the proposed method is demonstrated on applications arising from arm robotic model and image restoration problems.

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A Structured Fletcher-Revees Spectral Conjugate Gradient Method for Unconstrained Optimization with Application in Robotic Model

Salihu,

Kumam,

Awwal

et al. 2023

Oper. Res. Forum

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Two modified PRP conjugate gradient methods and their global convergence for unconstrained optimization

Cited by 3 publications

References 14 publications

A sufficient descent hybrid conjugate gradient method without line search consideration and application

A sufficient descent hybrid conjugate gradient method without line search consideration and application

The global convergence of spectral RMIL conjugate gradient method for unconstrained optimization with applications to robotic model and image recovery

A Structured Fletcher-Revees Spectral Conjugate Gradient Method for Unconstrained Optimization with Application in Robotic Model

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