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Convergence of symmetric rank-one method based on modified Quasi-Newton equation

In this paper we investigate on convergence rate of a modified symmetric rank-one (SR1) method for unconstrained optimization problems. In general, the modified SR1 method incorporates a modified secant equation into the standard SR1 method. Also a restart procedure is applied to avoid the loss of...

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Main Authors: Khiyabani, Farzin Modarres, Abu Hassan, Malik, Leong, Wah June
Format: Article
Language:English
Published: Canadian Center of Science and Education 2010
Online Access:http://psasir.upm.edu.my/id/eprint/13792/1/Convergence%20of%20symmetric%20rank.pdf
http://psasir.upm.edu.my/id/eprint/13792/
http://www.ccsenet.org/journal/index.php/jmr/article/view/4702
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spelling my.upm.eprints.137922015-09-22T06:41:51Z http://psasir.upm.edu.my/id/eprint/13792/ Convergence of symmetric rank-one method based on modified Quasi-Newton equation Khiyabani, Farzin Modarres Abu Hassan, Malik Leong, Wah June In this paper we investigate on convergence rate of a modified symmetric rank-one (SR1) method for unconstrained optimization problems. In general, the modified SR1 method incorporates a modified secant equation into the standard SR1 method. Also a restart procedure is applied to avoid the loss of positive definiteness and zero denominator. A remarkable feature of the modified SR1 method is that it possesses at most $n+1$-step $q$-superlinearly convergent and $2n$-step quadratic convergent without uniformly independent assumptions of steps. Canadian Center of Science and Education 2010-08 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/13792/1/Convergence%20of%20symmetric%20rank.pdf Khiyabani, Farzin Modarres and Abu Hassan, Malik and Leong, Wah June (2010) Convergence of symmetric rank-one method based on modified Quasi-Newton equation. Journal of Mathematics Research, 2 (3). pp. 97-102. ISSN 1916-9795; ESSN: 1916-9809 http://www.ccsenet.org/journal/index.php/jmr/article/view/4702 10.5539/jmr.v2n3p97
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 In this paper we investigate on convergence rate of a modified symmetric rank-one (SR1) method for unconstrained optimization problems. In general, the modified SR1 method incorporates a modified secant equation into the standard SR1 method. Also a restart procedure is applied to avoid the loss of positive definiteness and zero denominator. A remarkable feature of the modified SR1 method is that it possesses at most $n+1$-step $q$-superlinearly convergent and $2n$-step quadratic convergent without uniformly independent assumptions of steps.
format Article
author Khiyabani, Farzin Modarres
Abu Hassan, Malik
Leong, Wah June
spellingShingle Khiyabani, Farzin Modarres
Abu Hassan, Malik
Leong, Wah June
Convergence of symmetric rank-one method based on modified Quasi-Newton equation
author_facet Khiyabani, Farzin Modarres
Abu Hassan, Malik
Leong, Wah June
author_sort Khiyabani, Farzin Modarres
title Convergence of symmetric rank-one method based on modified Quasi-Newton equation
title_short Convergence of symmetric rank-one method based on modified Quasi-Newton equation
title_full Convergence of symmetric rank-one method based on modified Quasi-Newton equation
title_fullStr Convergence of symmetric rank-one method based on modified Quasi-Newton equation
title_full_unstemmed Convergence of symmetric rank-one method based on modified Quasi-Newton equation
title_sort convergence of symmetric rank-one method based on modified quasi-newton equation
publisher Canadian Center of Science and Education
publishDate 2010
url http://psasir.upm.edu.my/id/eprint/13792/1/Convergence%20of%20symmetric%20rank.pdf
http://psasir.upm.edu.my/id/eprint/13792/
http://www.ccsenet.org/journal/index.php/jmr/article/view/4702
_version_ 1643825437053288448
score 13.211869

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