A Scaled Dai–Yuan Projection-Based Conjugate Gradient Method for Solving Monotone Equations with Applications

Althobaiti, Ali; Sabi’u, Jamilu; Emadifar, Homan; Junsawang, Prem; Sahoo, Soubhagya Kumar

doi:10.3390/sym14071401

Cited by 5 publications

(3 citation statements)

References 36 publications

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“…where δ ∈ (0, 0.5) and σ ∈ (δ, 1) are constants. According to the search direction (30) and the Wolfe conditions ( 31) and ( 32), we present the explicit steps of the (CGCG) technique, as follows. Now, we present some numerical facts relating to the above parameters, allowing us to discuss the global convergence and descent properties of the CGCG method.…”

Section: Algorithm 4 Cgcg-hz Algorithmmentioning

confidence: 99%

“…Additionally, CG parameters have shown remarkable superiority in solving problems involving systems of nonlinear equations (see, for example, [26][27][28][29][30][31][32][33][34][35]). According to previous successful uses of CG techniques to solve different applications problems, many authors have adapted CG methods such that they are capable of dealing with image restoration problems (see, for example, [25,[35][36][37][38][39][40][41][42][43]).…”

Section: Introductionmentioning

confidence: 99%

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A Family of Developed Hybrid Four-Term Conjugate Gradient Algorithms for Unconstrained Optimization with Applications in Image Restoration

Ali

Mahdi

2023

Symmetry

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The most important advantage of conjugate gradient methods (CGs) is that these methods have low memory requirements and convergence speed. This paper contains two main parts that deal with two application problems, as follows. In the first part, three new parameters of the CG methods are designed and then combined by employing a convex combination. The search direction is a four-term hybrid form for modified classical CG methods with some newly proposed parameters. The result of this hybridization is the acquisition of a newly developed hybrid CGCG method containing four terms. The proposed CGCG has sufficient descent properties. The convergence analysis of the proposed method is considered under some reasonable conditions. A numerical investigation is carried out for an unconstrained optimization problem. The comparison between the newly suggested algorithm (CGCG) and five other classical CG algorithms shows that the new method is competitive with and in all statuses superior to the five methods in terms of efficiency reliability and effectiveness in solving large-scale, unconstrained optimization problems. The second main part of this paper discusses the image restoration problem. By using the adaptive median filter method, the noise in an image is detected, and then the corrupted pixels of the image are restored by using a new family of modified hybrid CG methods. This new family has four terms: the first is the negative gradient; the second one consists of either the HS-CG method or the HZ-CG method; and the third and fourth terms are taken from our proposed CGCG method. Additionally, a change in the size of the filter window plays a key role in improving the performance of this family of CG methods, according to the noise level. Four famous images (test problems) are used to examine the performance of the new family of modified hybrid CG methods. The outstanding clearness of the restored images indicates that the new family of modified hybrid CG methods has reliable efficiency and effectiveness in dealing with image restoration problems.

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Section: Algorithm 4 Cgcg-hz Algorithmmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Family of Developed Hybrid Four-Term Conjugate Gradient Algorithms for Unconstrained Optimization with Applications in Image Restoration

Ali

Mahdi

2023

Symmetry

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“…The authors proved the global convergence of the scheme under mild assumptions. Only recently, Alhobaiti et al [ 51 ] proposed two scaled DY-type algorithms for solving ( 14 ), where two different approaches were applied to compute the scaling parameter. The authors also showed that both methods satisfy ( 7 ) irrespective of the line search strategy used.…”

Section: Introductionmentioning

confidence: 99%

An efficient Dai-Yuan projection-based method with application in signal recovery

Sabi’u,

Balili,

Emadifar

2024

PLoS ONE

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The Dai and Yuan conjugate gradient (CG) method is one of the classical CG algorithms using the numerator ‖gk+1‖2. When the usual Wolfe line search is used, the algorithm is shown to satisfy the descent condition and to converge globally when the Lipschitz condition is assumed. Despite these two advantages, the Dai-Yuan algorithm performs poorly numerically due to the jamming problem. This work will present an efficient variant of the Dai-Yuan CG algorithm that solves a nonlinear constrained monotone system (NCMS) and resolves the aforementioned problems. Our variant algorithm, like the unmodified version, converges globally when the Lipschitz condition and sufficient descent requirements are satisfied, regardless of the line search method used. Numerical computations utilizing algorithms from the literature show that this variant algorithm is numerically robust. Finally, the variant algorithm is used to reconstruct sparse signals in compressed sensing (CS) problems.

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Improved Dai-Yuan iterative schemes for convex constrained monotone nonlinear systems

Ahmed,

Waziri,

Halilu

et al. 2024

Math Sci

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A Scaled Dai–Yuan Projection-Based Conjugate Gradient Method for Solving Monotone Equations with Applications

Cited by 5 publications

References 36 publications

A Family of Developed Hybrid Four-Term Conjugate Gradient Algorithms for Unconstrained Optimization with Applications in Image Restoration

A Family of Developed Hybrid Four-Term Conjugate Gradient Algorithms for Unconstrained Optimization with Applications in Image Restoration

An efficient Dai-Yuan projection-based method with application in signal recovery

Improved Dai-Yuan iterative schemes for convex constrained monotone nonlinear systems

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