Two Descent Dai-Yuan Conjugate Gradient Methods for Systems of Monotone Nonlinear Equations

Waziri, Mohammed Yusuf; Ahmed, Kabiru

doi:10.1007/s10915-021-01713-7

Cited by 20 publications

(8 citation statements)

References 61 publications

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“…In addition to their original authors, the issue of global convergence of methods (5) has also been investigated by some researchers like Al-Baali [40] and Gilbert and Nocedal [41]. Likewise, for all the CG directions that are presented in previous paragraph, the authors proved global convergence under necessary line searches techniques such as Armijo [14,16,20,29], week Wolfe-Powell [15-18, 21, 23, 24, 26, 27, 30, 35], strong Wolfe-Powell [12,16,19,22,25,28,31], modifications of these three techniques [13,[32][33][34] or some backtracking algorithms [36][37][38][39].…”

Section: Introductionmentioning

confidence: 86%

“…Furthermore, some researchers used techniques like quasi-Newton [26][27][28], regularization [29,30], a combination of above methods [31][32][33] or alternative techniques [34,35] and introduced appropriate CG methods to solve optimization problems. Similarly, there exist plenty of CG algorithms that are created to solve systems of nonlinear equations [36][37][38][39].…”

Section: Introductionmentioning

confidence: 99%

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Solving large scale unconstrained optimization problems with an efficient conjugate gradient class

Bojari

Paripour

2023

Preprint

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‎The main goal of this paper is to introduce an appropriate conjugate gradient class to solve unconstrained optimization problems‎. ‎The presented class enjoys the benefits of having three free parameters‎, ‎its directions are descent and it can fulfill the Dai-Liao conjugacy condition‎. ‎Global convergence property of the new class is proved under weak-Wolfe-Powell line search technique‎. ‎Numerical efficiency of the proposed class is confirmed in two sets of experiments including 210 test problems and ten disparate conjugate gradient methods‎. 2020 MSC: 90C06, 90C30, 90C26

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Section: Introductionmentioning

confidence: 86%

Section: Introductionmentioning

confidence: 99%

Solving large scale unconstrained optimization problems with an efficient conjugate gradient class

Bojari

Paripour

2023

Preprint

View full text Add to dashboard Cite

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“…Each of these methods used the concept of the projection technique and addressed the largescale system of monotone equations efficiently with some applications. Some recent papers on methods for solving convex constrained monotone systems can also be found in [28][29][30][31] and the references therein. Inspired by the success of these algorithms and the descent three-term conjugate gradient direction [32], we will propose a modified CG parameter by adopting the Birgin and Mart ínez [33] strategy, we will further use the proposed CG parameter and suggest a robust spectral three-term CG algorithm for solving the large-scale monotone equations with convex constraints with an application in image recovery.…”

Section: Consider the Systemmentioning

confidence: 99%

Scaled Three-Term Conjugate Gradient Methods for Solving Monotone Equations with Application

et al. 2022

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In this paper, we derived a modified conjugate gradient (CG) parameter by adopting the Birgin and Marti´nez strategy using the descent three-term CG direction and the Newton direction. The proposed CG parameter is applied and suggests a robust algorithm for solving constrained monotone equations with an application to image restoration problems. The global convergence of this algorithm is established using some proper assumptions. Lastly, the numerical comparison with some existing algorithms shows that the proposed algorithm is a robust approach for solving large-scale systems of monotone equations. Additionally, the proposed CG parameter can be used to solve the symmetric system of nonlinear equations as well as other relevant classes of nonlinear equations.

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“…Recently, Sabi'u et al [51] extended the Hager-Zhang scheme to solve system of monotone nonlinear equations with convex constraint, by obtaining two other choices for the Hager-Zhang parameter using singular value approach. For other recent advances in the literature, the reader is referred to [19,[53][54][55][56][57][58][59][60]. For this article, two other adaptations of HZ method, which are extension of the works in [48,50,51] are presented for solving convex constrained monotone nonlinear equations.…”

Section: Introductionmentioning

confidence: 99%

Two new Hager–Zhang iterative schemes with improved parameter choices for monotone nonlinear systems and their applications in compressed sensing

et al. 2022

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Notwithstanding its efficiency and nice attributes, most research on the iterative scheme by Hager and Zhang [Pac. J. Optim. 2(1) (2006) 35-58] are focused on unconstrained minimization problems. Inspired by this and recent works by Waziri et al. [Appl. Math. Comput. 361(2019) 645-660], Sabi’u et al. [Appl. Numer. Math. 153(2020) 217-233], and Sabi’u et al. [Int. J. Comput. Meth, doi:10.1142/S0219876220500437], this paper extends the Hager-Zhang (HZ) approach to nonlinear monotone systems with convex constraint. Two new HZ-type iterative methods are developed by combining the prominent projection method by Solodov and Svaiter [Springer, pp 355-369, 1998] with HZ-type search directions, which are obtained by developing two new parameter choices for the Hager-Zhang scheme. The first choice, is obtained by minimizing the condition number of a modified HZ direction matrix, while the second choice is realized using singular value analysis and minimizing the spectral condition number of the nonsingular HZ search direction matrix. Interesting properties of the schemes include solving non-smooth functions and generating descent directions. Using standard assumptions, the methods’ global convergence are obtained and numerical experiments with recent methods in the literature, indicate that the methods proposed are promising. The schemes effectiveness are further demonstrated by their applications to sparse signal and image reconstruction problems, where they outperform some recent schemes in the literature.

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Two Descent Dai-Yuan Conjugate Gradient Methods for Systems of Monotone Nonlinear Equations

Cited by 20 publications

References 61 publications

Solving large scale unconstrained optimization problems with an efficient conjugate gradient class

Solving large scale unconstrained optimization problems with an efficient conjugate gradient class

Scaled Three-Term Conjugate Gradient Methods for Solving Monotone Equations with Application

Two new Hager–Zhang iterative schemes with improved parameter choices for monotone nonlinear systems and their applications in compressed sensing

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