A new diagonal gradient-type method for large scale unconstrained optimization

The main focus of this paper is to derive new diagonal updating scheme via the direct weak secant equation. This new scheme allows us to improve the accuracy of the Hessian's approximation and is also capable to utilize information gathered about the function in previous iterations. It follows...

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Main Authors: Farid, Mahboubeh, Leong, Wah June, Zheng, Lihong
Format: Article
Language:English
Published: Politechnica University of Bucharest 2013
Online Access:http://psasir.upm.edu.my/id/eprint/30325/1/A%20new%20diagonal%20gradient.pdf
http://psasir.upm.edu.my/id/eprint/30325/
http://www.scientificbulletin.upb.ro/SeriaA_-_Matematica_si_fizica_aplicate.php?page=revistaonline&a=2&arh_an=2013&arh_ser=A&arh_nr=1
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Institution: Universiti Putra Malaysia
Language: English
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spelling my.upm.eprints.303252019-10-09T08:23:02Z http://psasir.upm.edu.my/id/eprint/30325/ A new diagonal gradient-type method for large scale unconstrained optimization Farid, Mahboubeh Leong, Wah June Zheng, Lihong The main focus of this paper is to derive new diagonal updating scheme via the direct weak secant equation. This new scheme allows us to improve the accuracy of the Hessian's approximation and is also capable to utilize information gathered about the function in previous iterations. It follows by an scaling approach that employs scaling parameter based upon the proposed weak secant equation to guarantee the positive definiteness of the Hessian's approximation. Moreover, we also prove the convergence of the proposed method under a simple monotone strategy. Numerical results show that the method is promising and frequently outperforms its competitors. Politechnica University of Bucharest 2013 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/30325/1/A%20new%20diagonal%20gradient.pdf Farid, Mahboubeh and Leong, Wah June and Zheng, Lihong (2013) A new diagonal gradient-type method for large scale unconstrained optimization. UPB Scientific Bulletin, Series A: Applied Mathematics and Physics, 75 (1). pp. 57-64. ISSN 1223-7027 http://www.scientificbulletin.upb.ro/SeriaA_-_Matematica_si_fizica_aplicate.php?page=revistaonline&a=2&arh_an=2013&arh_ser=A&arh_nr=1
institution Universiti Putra Malaysia
building UPM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Putra Malaysia
content_source UPM Institutional Repository
url_provider http://psasir.upm.edu.my/
language English
description The main focus of this paper is to derive new diagonal updating scheme via the direct weak secant equation. This new scheme allows us to improve the accuracy of the Hessian's approximation and is also capable to utilize information gathered about the function in previous iterations. It follows by an scaling approach that employs scaling parameter based upon the proposed weak secant equation to guarantee the positive definiteness of the Hessian's approximation. Moreover, we also prove the convergence of the proposed method under a simple monotone strategy. Numerical results show that the method is promising and frequently outperforms its competitors.
format Article
author Farid, Mahboubeh
Leong, Wah June
Zheng, Lihong
spellingShingle Farid, Mahboubeh
Leong, Wah June
Zheng, Lihong
A new diagonal gradient-type method for large scale unconstrained optimization
author_facet Farid, Mahboubeh
Leong, Wah June
Zheng, Lihong
author_sort Farid, Mahboubeh
title A new diagonal gradient-type method for large scale unconstrained optimization
title_short A new diagonal gradient-type method for large scale unconstrained optimization
title_full A new diagonal gradient-type method for large scale unconstrained optimization
title_fullStr A new diagonal gradient-type method for large scale unconstrained optimization
title_full_unstemmed A new diagonal gradient-type method for large scale unconstrained optimization
title_sort new diagonal gradient-type method for large scale unconstrained optimization
publisher Politechnica University of Bucharest
publishDate 2013
url http://psasir.upm.edu.my/id/eprint/30325/1/A%20new%20diagonal%20gradient.pdf
http://psasir.upm.edu.my/id/eprint/30325/
http://www.scientificbulletin.upb.ro/SeriaA_-_Matematica_si_fizica_aplicate.php?page=revistaonline&a=2&arh_an=2013&arh_ser=A&arh_nr=1
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