A Modified Conjugate Descent Projection Method for Monotone Nonlinear Equations and Image Restoration

Aji, Sani; Siricharoen, Punnarai; Abubakar, Auwal Bala; Yahaya, Mahmoud Muhammad

doi:10.1109/access.2020.3020334

Cited by 16 publications

(8 citation statements)

References 59 publications

(55 reference statements)

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“…For the methods compared with, all parameters are as given in MCDPM proposed by Aji et al [4], LSSCG presented by Yuan et al [28], PDY established by Liu and Feng [18], and Algorithm 2.1 by Yan et al [26], respectively. Iterations are terminated when ∥E k ∥ ≤ 10 −5 .…”

Section: Resultsmentioning

confidence: 99%

A solution method for nonlinear monotone equations via hybrid spectral conjugate gradient and signal recovery problems

Yusuf

Manjak

Mohammad

et al. 2023

Preprint

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In this paper, we propose a solution method via hybrid spectral conjugate gradient and signal recovery problem (ANHSCG) to solve nonlinear monotone equations. This has been done using the hybrid conjugate gradient (CG) parameters of Dai-Yuan (DY), conjugate descent (CD), Hestenes-Stiefel (HS), Liu-Storey (LS) and the corresponding search direction of spectral conjugate gradient method. The search direction has proved to be adequately descent regardless of the step-size. Under reasonable assumptions, the convergence of the algorithm is established. Additionally, numerical tests are run on a set of benchmark test problems to illustrate the effectiveness and competitiveness of the new algorithm compared with other existing alternatives. Finally, some applications of the proposed algorithm is explored. Mathematics Subject Classification: 65K05, 90C52, 90C26

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Section: Resultsmentioning

confidence: 99%

A solution method for nonlinear monotone equations via hybrid spectral conjugate gradient and signal recovery problems

Yusuf

Manjak

Mohammad

et al. 2023

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…Many variants based on conjugate gradient methods have been proposed in literature. For example, articles [16,111,55,112] propose new methods which combine hyperplane projection techniques with the conjugate gradient method to solve systems of monotone nonlinear equations (SNEs which satisfy the inequality in Eq. ( 4)).…”

Section: Local Search Methodsmentioning

confidence: 99%

“…Finding one or more solutions to a SNE is a challenging and ubiquitous task faced in many fields including chemistry [1,2,3], chemical engineering [4], automotive steering [5], power flow [6,7], large-scale integrated circuit designs [8], climate modeling [9], materials engineering [10], robotics [11,12,13,14], nuclear engineering [15], image restoration [16], protein interaction networks [8], neurophysiology [17], economics [18], finance [19], applied mathematics [20], physics [21], finding string vacua [22], machine learning [23,24], and geodesy [25,26] among others. The problem of solving even a system of polynomial equations has been proven to be NP-hard [27].…”

Section: Introductionmentioning

confidence: 99%

Survey of Methods for Solving Systems of Nonlinear Equations, Part II: Optimization Based Approaches

Kotsireas¹,

Pardalos²,

Semenov³

et al. 2022

Preprint

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This paper presents a comprehensive survey of methods which can be utilized to search for solutions to systems of nonlinear equations (SNEs). Our objectives with this survey are to synthesize pertinent literature in this field by presenting a thorough description and analysis of the known methods capable of finding one or many solutions to SNEs, and to assist interested readers seeking to identify solution techniques which are well suited for solving the various classes of SNEs which one may encounter in real world applications.To accomplish these objectives, we present a multi-part survey. In part one, we focused on root-finding approaches which can be used to search for solutions to a SNE without transforming it into an optimization problem. In part two, we introduce the various transformations which have been utilized to transform a SNE into an optimization problem, and we discuss optimization algorithms which can then be used to search for solutions. We emphasize the important characteristics of each method, and we discuss promising directions for future research. In part three, we will present a robust quantitative comparative analysis of methods capable of searching for solutions to SNEs.

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“…designs [8], climate modeling [9], materials engineering [10], robotics [11,12,13,14], nuclear engineering [15], image restoration [16], protein interaction networks [8], neurophysiology [17], economics [18], finance [19], applied mathematics [20], physics [21], finding string vacua [22], machine learning [23,24], geometric constraint solving (used in computer aided design) [25], and geodesy [26,27] among others. The problem of solving even a system of polynomial equations has been proven to be NP-hard [28].…”

Section: Introductionmentioning

confidence: 99%

Survey of Methods for Solving Systems of Nonlinear Equations, Part I: Root-finding Approaches

Kotsireas¹,

Pardalos²,

Semenov³

et al. 2022

Preprint

View full text Add to dashboard Cite

This paper presents a comprehensive survey of methods which can be utilized to search for solutions to systems of nonlinear equations (SNEs). Our objectives with this survey are to synthesize pertinent literature in this field by presenting a thorough description and analysis of the known methods capable of finding one or many solutions to SNEs, and to assist interested readers seeking to identify solution techniques which are well suited for solving the various classes of SNEs which one may encounter in real world applications.To accomplish these objectives, we present a multi-part survey. In part one, we focus on root-finding approaches which can be used to search for solutions to a SNE without transforming it into an optimization problem. In part two, we will introduce the various transformations which have been utilized to transform a SNE into an optimization problem, and we discuss optimization algorithms which can then be used to search for solutions. In part three, we will present a robust quantitative comparative analysis of methods capable of searching for solutions to SNEs.

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A Modified Conjugate Descent Projection Method for Monotone Nonlinear Equations and Image Restoration

Cited by 16 publications

References 59 publications

A solution method for nonlinear monotone equations via hybrid spectral conjugate gradient and signal recovery problems

A solution method for nonlinear monotone equations via hybrid spectral conjugate gradient and signal recovery problems

Survey of Methods for Solving Systems of Nonlinear Equations, Part II: Optimization Based Approaches

Survey of Methods for Solving Systems of Nonlinear Equations, Part I: Root-finding Approaches

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