Two New PRP Conjugate Gradient Algorithms for Minimization Optimization Models

Yuan, Gonglin; Duan, Xiabin; Liu, Wenjie; Wang, Xiaoliang; Cui, Zengru; Zhou, Sheng

doi:10.1371/journal.pone.0140071

Cited by 18 publications

(4 citation statements)

References 48 publications

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“…As a result, it is required to build original algorithms or approaches in order to tackle these difficulties. As a result, Yuan et al [18]- [21]. Describe a number of non-linear CG algorithms that can be used for non-smooth optimization problems.…”

Section: Resultsmentioning

confidence: 99%

Modified three-term conjugate gradient algorithm and its applications in image restoration

Ibrahim¹,

Khudhur²

2022

IJEECS

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In image restoration, the goal is often to bring back a high-quality version of an image from a lower-quality copy of it. In this article, we will investigate one kind of recovery issue, namely recovering photos that have been blurred by noise in digital photographs (sometimes known as "salt and pepper" noise). When subjected to noise at varying frequencies and intensities (30,50,70,90). In this paper, we used the conjugate gradient algorithm to Restorative images and remove noise from them, we developed the conjugate gradient algorithm with three limits using the conjugate condition of Dai and Liao, where the new algorithm achieved the conditions for descent and global convergence under some assumptions. According to the results of the numerical analysis, the recently created approach is unequivocally superior to both the fletcher and reeves (FR) method and the fletcher and reeves three-term (TTFR) metod. Use the structural similarity index measure (SSIM), which is used to measure image quality and the higher its value, the better the result. The original image was compared with all the noisy images and each according to the percentage of noise as well as the images processed with the four methods.

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Section: Resultsmentioning

confidence: 99%

Modified three-term conjugate gradient algorithm and its applications in image restoration

Ibrahim¹,

Khudhur²

2022

IJEECS

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“…One of the most attractive features of each numerical algorithm is how the procedure deals with large-scale systems of nonlinear equations. Recently, Gonglin Yuan et al [14,15] proposed conjugate gradient algorithms with global convergence under suitable conditions that possess some good properties for solving unconstrained optimization problems.…”

Section: Introductionmentioning

confidence: 99%

Efficient Two-Step Fifth-Order and Its Higher-Order Algorithms for Solving Nonlinear Systems with Applications

Sivakumar

Jayaraman

2019

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This manuscript presents a new two-step weighted Newton’s algorithm with convergence order five for approximating solutions of system of nonlinear equations. This algorithm needs evaluation of two vector functions and two Frechet derivatives per iteration. Furthermore, it is improved into a general multi-step algorithm with one more vector function evaluation per step, with convergence order 3 k + 5 , k ≥ 1 . Error analysis providing order of convergence of the algorithms and their computational efficiency are discussed based on the computational cost. Numerical implementation through some test problems are included, and comparison with well-known equivalent algorithms are presented. To verify the applicability of the proposed algorithms, we have implemented them on 1-D and 2-D Bratu problems. The presented algorithms perform better than many existing algorithms and are equivalent to a few available algorithms.

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“…The nonlinear system (1.1) has been proved to possess wildly different application fields in parameter estimating, function approximating, and nonlinear fitting, etc. At present, there exist many effective algorithms working in it, such as the traditional Gauss–Newton method [1, 9–11, 14, 16], the BFGS method [8, 23, 27, 29, 39, 43], the Levenberg–Marquardt method [6, 24, 42], the trust-region method [4, 26, 35, 41], the conjugate gradient algorithm [12, 25, 30, 38, 40], and the limited BFGS method [13, 28]. Here and in the next statement, for research convenience, suppose that has solution .…”

Section: Introductionmentioning

confidence: 99%

A tensor trust-region model for nonlinear system

Wang

Liu²

2018

J Inequal Appl

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It has turned out that the tensor expansion model has better approximation to the objective function than models of the normal second Taylor expansion. This paper conducts a study of the tensor model for nonlinear equations and it includes the following: (i) a three dimensional symmetric tensor trust-region subproblem model of the nonlinear equations is presented; (ii) the three dimensional symmetric tensor is replaced by interpolating function and gradient values from the most recent past iterate, which avoids the storage of the three dimensional symmetric tensor and decreases the workload of the computer; (iii) the limited BFGS quasi-Newton update is used instead of the second Jacobian matrix, which generates an inexpensive computation of a complex system; (iv) the global convergence is proved under suitable conditions. Numerical experiments are done to show that this proposed algorithm is competitive with the normal algorithm.

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Two New PRP Conjugate Gradient Algorithms for Minimization Optimization Models

Cited by 18 publications

References 48 publications

Modified three-term conjugate gradient algorithm and its applications in image restoration

Modified three-term conjugate gradient algorithm and its applications in image restoration

Efficient Two-Step Fifth-Order and Its Higher-Order Algorithms for Solving Nonlinear Systems with Applications

A tensor trust-region model for nonlinear system

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