Global convergence of new three terms conjugate gradient for unconstrained optimization

In this paper, a new formula of 𝛽𝑘 is suggested for the conjugate gradient method of solving unconstrained optimization problems based on three terms and step size of cubic. Our new proposed CG method has descent condition, sufficient descent condition, conjugacy condition, and global convergence pr...

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Autores principales:	Ahmed Anwer Mustafa, Salah Gazi Shareef
Formato:	article
Lenguaje:	EN
Publicado:	Refaad 2021
Materias:	conjugate gradient method descent condition sufficient descent conjugacy condition global convergent unconstrained optimizations Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/6191ebe61c8745298d03806b934bc291
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spelling	oai:doaj.org-article:6191ebe61c8745298d03806b934bc2912021-11-13T17:25:23ZGlobal convergence of new three terms conjugate gradient for unconstrained optimization10.31559/glm2021.11.1.12519-92692519-9277https://doaj.org/article/6191ebe61c8745298d03806b934bc2912021-09-01T00:00:00Zhttps://www.refaad.com/Files/GLM/GLM-11-1-1.pdfhttps://doaj.org/toc/2519-9269https://doaj.org/toc/2519-9277In this paper, a new formula of 𝛽𝑘 is suggested for the conjugate gradient method of solving unconstrained optimization problems based on three terms and step size of cubic. Our new proposed CG method has descent condition, sufficient descent condition, conjugacy condition, and global convergence properties. Numerical comparisons with two standard conjugate gradient algorithms show that this algorithm is very effective depending on the number of iterations and the number of functions evaluated.Ahmed Anwer MustafaSalah Gazi ShareefRefaadarticleconjugate gradient methoddescent conditionsufficient descentconjugacy conditionglobal convergentunconstrained optimizationsMathematicsQA1-939ENGeneral Letters in Mathematics , Vol 11, Iss 1, Pp 1-9 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	conjugate gradient method descent condition sufficient descent conjugacy condition global convergent unconstrained optimizations Mathematics QA1-939
spellingShingle	conjugate gradient method descent condition sufficient descent conjugacy condition global convergent unconstrained optimizations Mathematics QA1-939 Ahmed Anwer Mustafa Salah Gazi Shareef Global convergence of new three terms conjugate gradient for unconstrained optimization
description	In this paper, a new formula of 𝛽𝑘 is suggested for the conjugate gradient method of solving unconstrained optimization problems based on three terms and step size of cubic. Our new proposed CG method has descent condition, sufficient descent condition, conjugacy condition, and global convergence properties. Numerical comparisons with two standard conjugate gradient algorithms show that this algorithm is very effective depending on the number of iterations and the number of functions evaluated.
format	article
author	Ahmed Anwer Mustafa Salah Gazi Shareef
author_facet	Ahmed Anwer Mustafa Salah Gazi Shareef
author_sort	Ahmed Anwer Mustafa
title	Global convergence of new three terms conjugate gradient for unconstrained optimization
title_short	Global convergence of new three terms conjugate gradient for unconstrained optimization
title_full	Global convergence of new three terms conjugate gradient for unconstrained optimization
title_fullStr	Global convergence of new three terms conjugate gradient for unconstrained optimization
title_full_unstemmed	Global convergence of new three terms conjugate gradient for unconstrained optimization
title_sort	global convergence of new three terms conjugate gradient for unconstrained optimization
publisher	Refaad
publishDate	2021
url	https://doaj.org/article/6191ebe61c8745298d03806b934bc291
work_keys_str_mv	AT ahmedanwermustafa globalconvergenceofnewthreetermsconjugategradientforunconstrainedoptimization AT salahgazishareef globalconvergenceofnewthreetermsconjugategradientforunconstrainedoptimization
_version_	1718430079461097472

Global convergence of new three terms conjugate gradient for unconstrained optimization

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