The Hager–Zhang conjugate gradient algorithm for large-scale nonlinear equations

Yuan, Gonglin; Wang, Bopeng; Zhou, Sheng

doi:10.1080/00207160.2018.1494825

Cited by 11 publications

(1 citation statement)

References 57 publications

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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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