A convergent modified HS-DY hybrid conjugate gradient method for unconstrained optimization problems

Mtagulwa, Peter; Kaelo, P.

doi:10.1080/02522667.2018.1424087

Cited by 15 publications

(5 citation statements)

References 20 publications

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“…For example, see [8]. The first search direction is usually the negative of the gradient which is the steepest descent direction, i.e.,…”

Section: Issn: 0067-2904mentioning

confidence: 99%

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New Class of Conjugate Gradient Methods for Removing Impulse Noise Images

Abbo,

Hassan

2023

Iraqi Journal of Science

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The conjugate coefficient optimal is the very establishment of a variety of conjugate gradient methods. This paper proposes a new class coefficient of conjugate gradient (CG) methods for impulse noise removal, which is based on the quadratic model. Our proposed method ensures descent independent of the accuracy of the line search and it is globally convergent under some conditions, Numerical experiments are also presented for the impulse noise removal in images.

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“…For example, see [8]. The first search direction is usually the negative of the gradient which is the steepest descent direction, i.e.,…”

Section: Issn: 0067-2904mentioning

confidence: 99%

“…Suppose that the assumptions hold and consider any conjugate gradient method (4) and ( 9), where k d a descent direction and k is obtained by the strong Wolfe line search ( 6) and (8).…”

Section: Lemmamentioning

confidence: 99%

New Class of Conjugate Gradient Methods for Removing Impulse Noise Images

Abbo,

Hassan

2023

Iraqi Journal of Science

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“…To improve the nature of CG approaches, an automatic switching technique between the two groups of the methods are more preferable (Salihu et al ., 2021). For these current combinations, some hybrid schemes suggested include: HS and DY schemes (Andrei, 2008), PRP and FR methods (Mtagulwa and Kaelo, 2019), LS and DY methods (Liu and Li, 2014), PRP and DY methods (Andrei, 2009), LS with other CG procedures (Ibrahim et al ., 2022; Salihu et al ., 2020), DL and DY methods (Hamel et al ., 2023). These algorithms are usually required to satisfy conjugacy conditions for their convergence result as well as numerical performance via some line search considerations.…”

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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“…One type of noise is known as salt-and-pepper noise, in which the noisy pixels can only accept the maximum and minimum pixel values possible within the dynamic range of the source image. The random-valued noise, which may have any random value between the maximum and minimum pixel values of dynamic range, is another type of impulsive noise [18]. One of the most significant issues in picture processing is the removal of above both noise.…”

Section: Introductionmentioning

confidence: 99%

Efficient New Conjugate Gradient Methods for Removing Impulse Noise Images

Hassan

Sadiq²

2022

Eur. J. Pure Appl. Math.

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In most applications, denoising image is fundamental to subsequent image processing operations. In this research, we derivation a new formula of conjugate gradient methods based on the quadratic model. The fact that the search direction created at each iteration of the proposed approach is descending and independent of the line search makes it interesting. The use of Wolfeconditions also determines the global convergence of the suggested approach. To prove the viability of the suggested approach, comparison tests on impulse noise reduction are given.

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A convergent modified HS-DY hybrid conjugate gradient method for unconstrained optimization problems

Cited by 15 publications

References 20 publications

New Class of Conjugate Gradient Methods for Removing Impulse Noise Images

New Class of Conjugate Gradient Methods for Removing Impulse Noise Images

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

Efficient New Conjugate Gradient Methods for Removing Impulse Noise Images

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