A derivative-free projection method for solving convex constrained monotone equations

Yuan, Naichang

doi:10.2306/scienceasia1513-1874.2017.43.195

Cited by 13 publications

(2 citation statements)

References 12 publications

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“…At this juncture, the report of a set of numerical experiments is presented to exhibit performance and efficiency of the methods proposed. We test the performances of Algorithm 1 (N I HZPM) and Algorithm 2 (NEHZPM) with the modified Hager-Zhang methods in [2,51,68] and the efficient projected gradient method in [55] all of which are called MHZM1, MHZM2, CGD and EPGM for simplicity. For all the six methods, the backtracking line search defined in (2.7) was used, and the parameters for Algorithm 1 and Algorithm 2 are set as follows:…”

Section: Numerical Experiments and Comparisonsmentioning

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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Section: Numerical Experiments and Comparisonsmentioning

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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“…Since then many methods for solving system of nonlinear monotone equations have been proposed (see, e.g. [1,2,10,12,13,16,18,21,[23][24][25][26]29,30,32,35,[37][38][39]42], among others). Specifically, Ma and Wang [22] proposed a modified projection method for solving a system of monotone equations with convex constraints.…”

Section: Introductionmentioning

confidence: 99%

A diagonal PRP-type projection method for convex constrained nonlinear monotone equations

Mohammad¹

2021

Journal of Industrial &Amp; Management Optimization

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Iterative methods for nonlinear monotone equations do not require the differentiability assumption on the residual function. This special property of the methods makes them suitable for solving large-scale nonsmooth monotone equations. In this work, we present a diagonal Polak-Ribière-Polyk (PRP) conjugate gradient-type method for solving large-scale nonlinear monotone equations with convex constraints. The search direction is a combine form of a multivariate (diagonal) spectral method and a modified PRP conjugate gradient method. Proper safeguards are devised to ensure positive definiteness of the diagonal matrix associated with the search direction. Based on Lipschitz continuity and monotonicity assumptions the method is shown to be globally convergent. Numerical results are presented by means of comparative experiments with recently proposed multivariate spectral conjugate gradient-type method.

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Signal and image reconstruction with a double parameter Hager–Zhang‐type conjugate gradient method for system of nonlinear equations

Ahmed,

Waziri,

Halilu

et al. 2024

Numerical Linear Algebra App

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The one parameter conjugate gradient method by Hager and Zhang (Pac J Optim, 2(1):35–58, 2006) represents a family of descent iterative methods for solving large‐scale minimization problems. The nonnegative parameter of the scheme determines the weight of conjugacy and descent, and by extension, the numerical performance of the method. The scheme, however, does not converge globally for general nonlinear functions, and when the parameter approaches 0, the scheme reduces to the conjugate gradient method by Hestenes and Stiefel (J Res Nat Bur Stand, 49:409–436, 1952), which in practical sense does not perform well due to the jamming phenomenon. By carrying out eigenvalue analysis of an adaptive two parameter Hager–Zhang type method, a new scheme is presented for system of monotone nonlinear equations with its application in compressed sensing. The proposed scheme was inspired by nice attributes of the Hager–Zhang method and the various schemes designed with double parameters. The scheme is also applicable to nonsmooth nonlinear problems. Using fundamental assumptions, analysis of the global convergence of the scheme is conducted and preliminary report of numerical experiments carried out with the scheme and some recent methods indicate that the scheme is promising.

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A derivative-free projection method for solving convex constrained monotone equations

Cited by 13 publications

References 12 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

A diagonal PRP-type projection method for convex constrained nonlinear monotone equations

Signal and image reconstruction with a double parameter Hager–Zhang‐type conjugate gradient method for system of nonlinear equations

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