A New Modified Three-Term Conjugate Gradient Method with Sufficient Descent Property and Its Global Convergence

A new modified three-term conjugate gradient (CG) method is shown for solving the large scale optimization problems. The idea relates to the famous Polak-Ribière-Polyak (PRP) formula. As the numerator of PRP plays a vital role in numerical result and not having the jamming issue, PRP method is not g...

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Main Authors: Bakhtawar Baluch, Zabidin Salleh, Ahmad Alhawarat, U. A. M. Roslan
Format: Article
Language:English
Published: Wiley 2017-01-01
Series:Journal of Mathematics
Online Access:http://dx.doi.org/10.1155/2017/2715854
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author Bakhtawar Baluch
Zabidin Salleh
Ahmad Alhawarat
U. A. M. Roslan
author_facet Bakhtawar Baluch
Zabidin Salleh
Ahmad Alhawarat
U. A. M. Roslan
author_sort Bakhtawar Baluch
collection DOAJ
description A new modified three-term conjugate gradient (CG) method is shown for solving the large scale optimization problems. The idea relates to the famous Polak-Ribière-Polyak (PRP) formula. As the numerator of PRP plays a vital role in numerical result and not having the jamming issue, PRP method is not globally convergent. So, for the new three-term CG method, the idea is to use the PRP numerator and combine it with any good CG formula’s denominator that performs well. The new modification of three-term CG method possesses the sufficient descent condition independent of any line search. The novelty is that by using the Wolfe Powell line search the new modification possesses global convergence properties with convex and nonconvex functions. Numerical computation with the Wolfe Powell line search by using the standard test function of optimization shows the efficiency and robustness of the new modification.
format Article
id doaj-art-3b19438213e64549817eec05cc2441af
institution Kabale University
issn 2314-4629
2314-4785
language English
publishDate 2017-01-01
publisher Wiley
record_format Article
series Journal of Mathematics
spelling doaj-art-3b19438213e64549817eec05cc2441af2025-02-03T05:50:28ZengWileyJournal of Mathematics2314-46292314-47852017-01-01201710.1155/2017/27158542715854A New Modified Three-Term Conjugate Gradient Method with Sufficient Descent Property and Its Global ConvergenceBakhtawar Baluch0Zabidin Salleh1Ahmad Alhawarat2U. A. M. Roslan3School of Informatics and Applied Mathematics, Universiti Malaysia Terengganu, 21030 Kuala Nerus, Terengganu, MalaysiaSchool of Informatics and Applied Mathematics, Universiti Malaysia Terengganu, 21030 Kuala Nerus, Terengganu, MalaysiaDepartment of Mathematics, College of Science, Al-Isra University, Amman, JordanSchool of Informatics and Applied Mathematics, Universiti Malaysia Terengganu, 21030 Kuala Nerus, Terengganu, MalaysiaA new modified three-term conjugate gradient (CG) method is shown for solving the large scale optimization problems. The idea relates to the famous Polak-Ribière-Polyak (PRP) formula. As the numerator of PRP plays a vital role in numerical result and not having the jamming issue, PRP method is not globally convergent. So, for the new three-term CG method, the idea is to use the PRP numerator and combine it with any good CG formula’s denominator that performs well. The new modification of three-term CG method possesses the sufficient descent condition independent of any line search. The novelty is that by using the Wolfe Powell line search the new modification possesses global convergence properties with convex and nonconvex functions. Numerical computation with the Wolfe Powell line search by using the standard test function of optimization shows the efficiency and robustness of the new modification.http://dx.doi.org/10.1155/2017/2715854
spellingShingle Bakhtawar Baluch
Zabidin Salleh
Ahmad Alhawarat
U. A. M. Roslan
A New Modified Three-Term Conjugate Gradient Method with Sufficient Descent Property and Its Global Convergence
Journal of Mathematics
title A New Modified Three-Term Conjugate Gradient Method with Sufficient Descent Property and Its Global Convergence
title_full A New Modified Three-Term Conjugate Gradient Method with Sufficient Descent Property and Its Global Convergence
title_fullStr A New Modified Three-Term Conjugate Gradient Method with Sufficient Descent Property and Its Global Convergence
title_full_unstemmed A New Modified Three-Term Conjugate Gradient Method with Sufficient Descent Property and Its Global Convergence
title_short A New Modified Three-Term Conjugate Gradient Method with Sufficient Descent Property and Its Global Convergence
title_sort new modified three term conjugate gradient method with sufficient descent property and its global convergence
url http://dx.doi.org/10.1155/2017/2715854
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