Modified Hager–Zhang conjugate gradient methods via singular value analysis for solving monotone nonlinear equations with convex constraint

Sabi’u, Jamilu; Shah, Abdullah; Waziri, Mohammed Yusuf; Ahmed, Kabiru

doi:10.1142/s0219876220500437

Cited by 26 publications

(15 citation statements)

References 48 publications

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“…The authors proved the methods are effective and converge globally under mild conditions. Recently, inspired by the work in [13,48,50], Sabi'u et al [51] proposed two other Hager-Zhang methods for convex constrained monotone systems with the following parameters:…”

Section: Preliminaries and The Proposed Methodsmentioning

confidence: 99%

“…Still, finding optimal values for θ k is an open problem for the one-parameter HZ method. So, with inspiration from the works in [48,50] and [51], we also propose two optimal choices, for the HZ parameter, and consequently present two modified HZ methods for nonlinear monotone systems with convex constraint, which are effective and always generate descent directions.…”

Section: Preliminaries and The Proposed Methodsmentioning

confidence: 99%

“…Sabi'u et al [50] improved on the work in [48] by obtaining other choices for the Hager-Zhang parameter in [49], which are employed to develop other versions of the scheme in [48]. 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].…”

Section: Introductionmentioning

confidence: 99%

“…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. This research is embarked upon due to the following considerations: i.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Preliminaries and The Proposed Methodsmentioning

confidence: 99%

Section: Preliminaries and The Proposed Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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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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“…Under mild conditions, global convergence of the scheme is proven. For further recent progress on addition methods, we refer the reader to [20,47,48,49,50,40,41,51,21,22] and the references therein.…”

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confidence: 99%

Modified Dai-Yuan iterative scheme for nonlinear systems and its application

Waziri¹,

Ahmed²,

Halilu³

et al. 2023

NACO

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<p style='text-indent:20px;'>By exploiting the idea employed in the spectral Dai-Yuan method by Xue et al. [IEICE Trans. Inf. Syst. 101 (12)2984-2990 (2018)] and the approach applied in the modified Hager-Zhang scheme for nonsmooth optimization [PLos ONE 11(10): e0164289 (2016)], we develop a Dai-Yuan type iterative scheme for convex constrained nonlinear monotone system. The scheme's algorithm is obtained by combining its search direction with the projection method [Kluwer Academic Publishers, pp. 355-369(1998)]. One of the new scheme's attribute is that it is derivative-free, which makes it ideal for solving non-smooth problems. Furthermore, we demonstrate the method's application in image de-blurring problems by comparing its performance with a recent effective method. By employing mild assumptions, global convergence of the scheme is determined and results of some numerical experiments show the method to be favorable compared to some recent iterative methods.</p>

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A derivative‐free scaling memoryless Broyden–Fletcher–Goldfarb–Shanno method for solving a system of monotone nonlinear equations

Ullah

Sabi’u

Shah

2021

Numerical Linear Algebra App

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This paper presents the two-parameter scaling memoryless Broyden-Fletcher-Goldfarb-Shanno (BFGS) method for solving a system of monotone nonlinear equations. The optimal values of the scaling parameters are obtained by minimizing the measure function involving all the eigenvalues of the memoryless BFGS matrix. The optimal values can be used in the analysis of the quasi-Newton method for ill-conditioned matrices. This algorithm can also be described as a combination of the projection technique and memoryless BGFS method.Global convergence of the method is provided. For validation and efficiency of the scheme, some test problems are computed and compared with existing results.

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Modified Hager–Zhang conjugate gradient methods via singular value analysis for solving monotone nonlinear equations with convex constraint

Cited by 26 publications

References 48 publications

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

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

Modified Dai-Yuan iterative scheme for nonlinear systems and its application

A derivative‐free scaling memoryless Broyden–Fletcher–Goldfarb–Shanno method for solving a system of monotone nonlinear equations

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