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Global convergence analysis of a nonlinear conjugate gradient method for unconstrained optimization problems

Background/Objectives: The Conjugate Gradient (CG) methods are the well-known iterative methods use for finding solutions to nonlinear system equations. There is need to address the jamming phenomenal facing the current class of this methods. Methods/Statistical Analysis: In order to address the sho...

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Main Authors: Abdullahi, I., Ahmad, R.
Format: Article
Published: Indian Society for Education and Environment 2016
Subjects:
QA Mathematics
Online Access:http://eprints.utm.my/id/eprint/74404/
https://www.scopus.com/inward/record.uri?eid=2-s2.0-84995757412&doi=10.17485%2fijst%2f2016%2fv9i41%2f90175&partnerID=40&md5=6b84f7ffdc527acffdd99d7be7278966
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spelling my.utm.744042017-11-29T23:58:35Z http://eprints.utm.my/id/eprint/74404/ Global convergence analysis of a nonlinear conjugate gradient method for unconstrained optimization problems Abdullahi, I. Ahmad, R. QA Mathematics Background/Objectives: The Conjugate Gradient (CG) methods are the well-known iterative methods use for finding solutions to nonlinear system equations. There is need to address the jamming phenomenal facing the current class of this methods. Methods/Statistical Analysis: In order to address the shortcomings, we work on the denominator of the Yao et al., CG method which is known to generate descent direction for objective functions by proposing an entire different CG coefficient which can easily switch in case jamming occurs by imposing some parameters thereby guarantee global convergence. Findings: The proposed CG formula performs better than classical methods as well as Yao et al. Under Wolfe line search condition, the convergence analysis of the proposed CG formula was established. Some benchmark problems from cute collections are used as basis of strength comparisons of the proposed formula against some other CG formulas. Effectiveness and efficiency of the obtained results for the proposed formula is clearly shown by adopting the performance profile of Dolan and More' which is one of most acceptable techniques of strength comparisons among methods. Application: Mathematicians and Engineers who are interested in finding solutions to large scale nonlinear equations can apply the method leading to global optimization dealing with best possible solutions ever for given problems. Indian Society for Education and Environment 2016 Article PeerReviewed Abdullahi, I. and Ahmad, R. (2016) Global convergence analysis of a nonlinear conjugate gradient method for unconstrained optimization problems. Indian Journal of Science and Technology, 9 (41). ISSN 0974-6846 https://www.scopus.com/inward/record.uri?eid=2-s2.0-84995757412&doi=10.17485%2fijst%2f2016%2fv9i41%2f90175&partnerID=40&md5=6b84f7ffdc527acffdd99d7be7278966
institution Universiti Teknologi Malaysia
building UTM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Teknologi Malaysia
content_source UTM Institutional Repository
url_provider http://eprints.utm.my/
topic QA Mathematics
spellingShingle QA Mathematics
Abdullahi, I.
Ahmad, R.
Global convergence analysis of a nonlinear conjugate gradient method for unconstrained optimization problems
description Background/Objectives: The Conjugate Gradient (CG) methods are the well-known iterative methods use for finding solutions to nonlinear system equations. There is need to address the jamming phenomenal facing the current class of this methods. Methods/Statistical Analysis: In order to address the shortcomings, we work on the denominator of the Yao et al., CG method which is known to generate descent direction for objective functions by proposing an entire different CG coefficient which can easily switch in case jamming occurs by imposing some parameters thereby guarantee global convergence. Findings: The proposed CG formula performs better than classical methods as well as Yao et al. Under Wolfe line search condition, the convergence analysis of the proposed CG formula was established. Some benchmark problems from cute collections are used as basis of strength comparisons of the proposed formula against some other CG formulas. Effectiveness and efficiency of the obtained results for the proposed formula is clearly shown by adopting the performance profile of Dolan and More' which is one of most acceptable techniques of strength comparisons among methods. Application: Mathematicians and Engineers who are interested in finding solutions to large scale nonlinear equations can apply the method leading to global optimization dealing with best possible solutions ever for given problems.
format Article
author Abdullahi, I.
Ahmad, R.
author_facet Abdullahi, I.
Ahmad, R.
author_sort Abdullahi, I.
title Global convergence analysis of a nonlinear conjugate gradient method for unconstrained optimization problems
title_short Global convergence analysis of a nonlinear conjugate gradient method for unconstrained optimization problems
title_full Global convergence analysis of a nonlinear conjugate gradient method for unconstrained optimization problems
title_fullStr Global convergence analysis of a nonlinear conjugate gradient method for unconstrained optimization problems
title_full_unstemmed Global convergence analysis of a nonlinear conjugate gradient method for unconstrained optimization problems
title_sort global convergence analysis of a nonlinear conjugate gradient method for unconstrained optimization problems
publisher Indian Society for Education and Environment
publishDate 2016
url http://eprints.utm.my/id/eprint/74404/
https://www.scopus.com/inward/record.uri?eid=2-s2.0-84995757412&doi=10.17485%2fijst%2f2016%2fv9i41%2f90175&partnerID=40&md5=6b84f7ffdc527acffdd99d7be7278966
_version_ 1643656850801950720
score 13.211869

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