Modified optimal Perry conjugate gradient method for solving system of monotone equations with applications
type: Item
instance of: scholarly article
title: Modified optimal Perry conjugate gradient method for solving system of monotone equations with applications
author: Jamilu Sabi'u
author: Abdullah Shah
author: Predrag S. Stanimirović
author: Branislav Ivanov
author: M. Y. Waziri
published in: Applied Numerical Mathematics
publication date: 2022-12-09T00:00:00Z
review text: The paper is devoted to large-scale monotone nonlinear equations. To solve such problems, the Newton and quasi-Newton methods are usually used due to their rapid convergence within the neighborhood of the solution set. The major drawbacks of these methods are operations with the Jacobian matrix at every iteration. Thus, researches have focused on spectral and conjugate gradient type methods due to their simplicity, minimum storage requirements, and better convergence properties which is important especially for solving large-scale problems. The authors propose a modified optimal Perry conjugate gradient method. An optimal choice for the scaled parameter is obtained by minimizing the difference between the largest and smallest eigenvalues of the search direction matrix. The method is incorporated with the hyperplane projection technique to exploit the advantages of the well-known predictor-corrector technique. The result is a robust algorithm for solving convex constrained monotone equations with applications in image and signal recovery. The global convergence of the proposed method is established using monotonicity and Lipschitz continuity assumptions. Numerical experiments are performed on convex constrained large-scale monotone equations and on applications in image and signal restoration problems. Comparisons of the results with other recent relevant methods show high efficiency of the proposed method.
reviewed by: Ctirad Matonoha
Mathematics Subject Classification ID: 65K05
Mathematics Subject Classification ID: 65H10
Mathematics Subject Classification ID: 90C06
Mathematics Subject Classification ID: 90C25
Mathematics Subject Classification ID: 15A18
zbMATH DE Number: 7630343
zbMATH Keywords: monotone equations
zbMATH Keywords: Perry conjugate gradient method
zbMATH Keywords: hyperplane
zbMATH Keywords: projection
zbMATH Keywords: eigenvalues
zbMATH Keywords: image restoration
zbMATH Keywords: signal restoration
zbMATH Keywords: global convergence
MaRDI profile type: Publication
full work available at URL: j.apnum.2022.10.016
OpenAlex ID: W4308745859
cites work: A descent Dai-Liao conjugate gradient method for nonlinear equations
cites work: A note on the spectral gradient projection method for nonlinear monotone equations with applications
cites work: A Perry-type derivative-free algorithm for solving nonlinear system of equations and minimizing ℓ1regularized problem
cites work: A descent family of Dai–Liao conjugate gradient methods
cites work: The Dai-Liao nonlinear conjugate gradient method with optimal parameter choices
cites work: Two-Point Step Size Gradient Methods
cites work: Q4488067
cites work: A PRP type method for systems of monotone equations
cites work: New conjugacy conditions and related nonlinear conjugate gradient methods
cites work: A Nonlinear Conjugate Gradient Method with a Strong Global Convergence Property
cites work: A modified Perry's conjugate gradient method-based derivative-free method for solving large-scale nonlinear monotone equations
cites work: Q3702408
cites work: Benchmarking optimization software with performance profiles.
cites work: Function minimization by conjugate gradients
cites work: A modified spectral PRP conjugate gradient projection method for solving large-scale monotone equations and its application in compressed sensing
cites work: Q5479892
cites work: Deblurring Images
cites work: Methods of conjugate gradients for solving linear systems
cites work: Newton-type Methods with Generalized Distances For Constrained Optimization
cites work: Self adaptive spectral conjugate gradient method for solving nonlinear monotone equations
cites work: Spectral residual method without gradient information for solving large-scale nonlinear systems of equations
cites work: A class of derivative-free methods for large-scale nonlinear monotone equations
cites work: Spectral DY-Type Projection Method for Nonlinear Monotone Systems of Equations
cites work: A new conjugate gradient projection method for convex constrained nonlinear equations
cites work: A methodology for solving chemical equilibrium systems
cites work: Q5500361
cites work: Q5652137
cites work: Inexact Newton methods for the nonlinear complementarity problem
cites work: Technical Note—A Modified Conjugate Gradient Algorithm
cites work: Q5563083
cites work: Two optimal Hager-Zhang conjugate gradient methods for solving monotone nonlinear equations
cites work: New hybrid conjugate gradient projection method for the convex constrained equations
cites work: Descent Perry conjugate gradient methods for systems of monotone nonlinear equations
cites work: A conjugate gradient method to solve convex constrained monotone equations with applications in compressive sensing
cites work: Non-smooth equations based method for \(\ell_1\)-norm problems with applications to compressed sensing
cites work: The global convergence of the Polak-Ribière-Polyak conjugate gradient algorithm under inexact line search for nonconvex functions
cites work: A conjugate gradient algorithm for large-scale nonlinear equations and image restoration problems
cites work: The PRP conjugate gradient algorithm with a modified WWP line search and its application in the image restoration problems
cites work: Spectral gradient projection method for solving nonlinear monotone equations
cites work: A descent modified Polak–Ribière–Polyak conjugate gradient method and its global convergence
cites work: Monotonicity of fixed point and normal mappings associated with variational inequality and its application
cites work: A conjugate gradient projection method for solving equations with convex constraints
cites work: A globally convergent BFGS method for nonlinear monotone equations without any merit functions
cites work: Superlinear convergence of a Newton-type algorithm for monotone equations
DOI: 10.1016/J.APNUM.2022.10.016
description: scientific article; zbMATH DE number 7630343