A New Hybrid Three-Term Conjugate Gradient Algorithm for Large-Scale Unconstrained Problems

Tian, Qi; Wang, Xiaoliang; Pang, Li-Ping; Zhang, Mingkun; Meng, Fan-Yun

doi:10.3390/math9121353

Cited by 10 publications

(2 citation statements)

References 39 publications

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“…Tian et al [56] suggested a new hybrid three-term CG approach without using a line search method. The authors of [56] designed the new hybrid descent three-term direction in the following form:…”

Section: Introductionmentioning

confidence: 99%

“…They proceeded to provide some remarks regarding their proposed directions. In addition, the authors of [56] successfully performed a convergence analysis of their newly proposed CG method (under certain conditions). The numerical outcomes demonstrate that the three-term CG method is more efficient and reliable in terms of solving large-scale unconstrained optimization problems compared to other methods.…”

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: Introductionmentioning

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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An improved descent Perry‐type algorithm for large‐scale unconstrained nonconvex problems and applications to image restoration problems

Wang,

Lv,

2024

Numerical Linear Algebra App

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Conjugate gradient methods are much effective for large‐scale unconstrained optimization problems by their simple computations and low memory requirements. The Perry conjugate gradient method has been considered to be one of the most efficient methods in the context of unconstrained minimization. However, a globally convergent result for general functions has not been established yet. In this paper, an improved three‐term Perry‐type algorithm is proposed which automatically satisfies the sufficient descent property independent of the accuracy of line search strategy. Under the standard Wolfe line search technique and a modified secant condition, the proposed algorithm is globally convergent for general nonlinear functions without convexity assumption. Numerical results compared with the Perry method for stability, two modified Perry‐type conjugate gradient methods and two effective three‐term conjugate gradient methods for large‐scale problems up to 300,000 dimensions indicate that the proposed algorithm is more efficient and reliable than the other methods for the testing problems. Additionally, we also apply it to some image restoration problems.

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A class of new three-term descent conjugate gradient algorithms for large-scale unconstrained optimization and applications to image restoration problems

Wang

Yuan²,

Pang³

2022

Numer Algor

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A New Hybrid Three-Term Conjugate Gradient Algorithm for Large-Scale Unconstrained Problems

Cited by 10 publications

References 39 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 improved descent Perry‐type algorithm for large‐scale unconstrained nonconvex problems and applications to image restoration problems

A class of new three-term descent conjugate gradient algorithms for large-scale unconstrained optimization and applications to image restoration problems

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