A modified nonlinear conjugate gradient algorithm for large-scale nonsmooth convex optimization
type: Item
instance of: scholarly article
title: A modified nonlinear conjugate gradient algorithm for large-scale nonsmooth convex optimization
zbMATH Open document ID: 1441.90159
author: Tsegay Giday Woldu
author: Hai-Bin Zhang
author: Xin Zhang
author: Yemane Hailu Fissuh
published in: Journal of Optimization Theory and Applications
publication date: 2020-04-07T00:00:00Z
review text: Nonlinear conjugate gradient methods (CG) are among the most preferred for solving large-scale smooth problems because of their simplicity and low memory requirement. This paper presents the modified CG method, which includes the advantages of the CG methods for solving large-scale nonsmooth convex optimization problems. This method has the strong global convergence property of Dai and Yuan (DY) method and numerical efficiency of Hestenes and Stiefel (HS) method. The new method uses the search direction, which generates sufficient descent property and belongs to a trust region. Numerical results indicate that the method performs very well.
Mathematics Subject Classification ID: 90C30
Mathematics Subject Classification ID: 90C25
Mathematics Subject Classification ID: 65K05
Mathematics Subject Classification ID: 90C52
zbMATH DE Number: 7187332
zbMATH Keywords: conjugate gradient method
zbMATH Keywords: Moreau-Yosida regularization
zbMATH Keywords: nonsmooth large-scale problems
zbMATH Keywords: global convergence
reviewed by: Nada Djuranović-Miličić
describes a project that uses: PNEW
describes a project that uses: LDGB
describes a project that uses: PDCO
MaRDI profile type: Publication
full work available at URL: s10957-020-01636-7
OpenAlex ID: W3006347222
cites work: Survey of Bundle Methods for Nonsmooth Optimization
cites work: Atomic Decomposition by Basis Pursuit
cites work: Comparison of formulations and solution methods for image restoration problems
cites work: Q4004158
cites work: Practical Aspects of the Moreau--Yosida Regularization: Theoretical Preliminaries
cites work: A Globally and Superlinearly Convergent Algorithm for Nonsmooth Convex Minimization
cites work: Monotone Operators and the Proximal Point Algorithm
cites work: Convergence analysis of some methods for minimizing a nonsmooth convex function
cites work: A family of variable metric proximal methods
cites work: Convergence analysis of a proximal newton method1
cites work: The Barzilai and Borwein gradient method with nonmonotone line search for nonsmooth convex optimization problems
cites work: A trust region method for nonsmooth convex optimization
cites work: Gradient trust region algorithm with limited memory BFGS update for nonsmooth convex minimization
cites work: Proximity control in bundle methods for convex nondifferentiable minimization
cites work: A bundle-Newton method for nonsmooth unconstrained minimization
cites work: Methods of descent for nondifferentiable optimization
cites work: Proximal level bundle methods for convex nondifferentiable optimization, saddle-point problems and variational inequalities
cites work: New limited memory bundle method for large-scale nonsmooth optimization
cites work: TWO MODIFIED HYBRID CONJUGATE GRADIENT METHODS BASED ON A HYBRID SECANT EQUATION
cites work: Methods of conjugate gradients for solving linear systems
cites work: Q5563083
cites work: Efficient generalized conjugate gradient algorithms. I: Theory
cites work: Function minimization by conjugate gradients
cites work: Q3882253
cites work: A Nonlinear Conjugate Gradient Method with a Strong Global Convergence Property
cites work: Q5479892
cites work: A modified Polak-Ribière-Polyak conjugate gradient algorithm for nonsmooth convex programs
cites work: A modified Hestenes and Stiefel conjugate gradient algorithm for large-scale nonsmooth minimizations and nonlinear equations
cites work: A modified PRP conjugate gradient algorithm with nonmonotone line search for nonsmooth convex optimization problems
cites work: A new smoothing modified three-term conjugate gradient method for \(l_1\)-norm minimization problem
cites work: The smoothing FR conjugate gradient method for solving a kind of nonsmooth optimization problem with \(l_1\)-norm
cites work: Convergence of some algorithms for convex minimization
cites work: Q3141900
cites work: Projected gradient methods for linearly constrained problems
cites work: Convergence Analysis of Some Algorithms for Solving Nonsmooth Equations
cites work: Optimization and nonsmooth analysis
cites work: The conjugate gradient method in extremal problems
cites work: A descent algorithm for nonsmooth convex optimization
cites work: Benchmarking optimization software with performance profiles.
DOI: 10.1007/S10957-020-01636-7
description: scientific article; zbMATH DE number 7187332