A new modified three-term Hestenes-Stiefel conjugate gradient method with sufficient descent property and its global convergence
type: Item
instance of: scholarly article
title: A new modified three-term Hestenes-Stiefel conjugate gradient method with sufficient descent property and its global convergence
zbMATH Open document ID: 1460.90205
DOI: 10.1155/2018/5057096
author: Bakhtawar Baluch
author: Zabidin Salleh
author: Ahmad Alhawarat
published in: Journal of Optimization
publication date: 2019-02-18T00:00:00Z
review text: Summary: This paper describes a modified three-term Hestenes-Stiefel (HS) method. The original HS method is the earliest conjugate gradient method. Although the HS method achieves global convergence using an exact line search, this is not guaranteed in the case of an inexact line search. In addition, the HS method does not usually satisfy the descent property. Our modified three-term conjugate gradient method possesses a sufficient descent property regardless of the type of line search and guarantees global convergence using the inexact Wolfe-Powell line search. The numerical efficiency of the modified three-term HS method is checked using 75 standard test functions. It is known that three-term conjugate gradient methods are numerically more efficient than two-term conjugate gradient methods. Importantly, this paper quantifies how much better the three-term performance is compared with two-term methods. Thus, in the numerical results, we compare our new modification with an efficient two-term conjugate gradient method. We also compare our modification with a state-of-the-art three-term HS method. Finally, we conclude that our proposed modification is globally convergent and numerically efficient.
Mathematics Subject Classification ID: 90C53
Mathematics Subject Classification ID: 65K10
Mathematics Subject Classification ID: 90C52
zbMATH DE Number: 7024762
describes a project that uses: L-BFGS
describes a project that uses: minpack
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2018/5057096
OpenAlex ID: W2893252565
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Wikidata QID: Q129184143
description: scientific article; zbMATH DE number 7024762