A new class of three-term conjugate gradient methods for solving unconstrained minimization problems

Volume 7, Issue 2, Article 4 - 2019

Authors: Alaa Luqman Ibrahim ;Salah Gazi Shareef

Copyright © 2019 . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Abstract

Conjugate gradient (CG) methods which are usually generate descent search directions, are beneficial for large-scale unconstrained optimization models, because of its low memory requirement and simplicity. This paper studies the three-term CG method for unconstrained optimization. The modified a three-term CG method based on the formal 𝒕∗ which is suggested by Kafaki and Ghanbari [11], and using some well-known CG formulas for unconstrained optimization. Our proposed method satisfies both (the descent and the sufficient descent) conditions. Furthermore, if we use the exact line search the new proposed is reduce to the classical CG method. The numerical results show that the suggested method is promising and exhibits a better numerical performance in comparison with the three- term (ZHS-CG) method from an implementation of the suggested method on some normal unconstrained optimization test functions.

How To Cite This Article

Alaa Luqman Ibrahim ;Salah Gazi Shareef (2019) A new class of three-term conjugate gradient methods for solving unconstrained minimization problems
General Letters in Mathematics Vol 7 (2) 79-86
https://doi.org/10.31559/glm2019.7.2.4