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...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Canadian Center of Science and Education
2010
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| Online Access: | http://psasir.upm.edu.my/id/eprint/13792/1/Convergence%20of%20symmetric%20rank.pdf |
| _version_ | 1796968512277708800 |
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| author | Khiyabani, Farzin Modarres Abu Hassan, Malik Leong, Wah June |
| author_facet | Khiyabani, Farzin Modarres Abu Hassan, Malik Leong, Wah June |
| author_sort | Khiyabani, Farzin Modarres |
| collection | UPM |
| 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. |
| first_indexed | 2024-03-06T07:29:24Z |
| format | Article |
| id | upm.eprints-13792 |
| institution | Universiti Putra Malaysia |
| language | English |
| last_indexed | 2024-03-06T07:29:24Z |
| publishDate | 2010 |
| publisher | Canadian Center of Science and Education |
| record_format | dspace |
| spelling | 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 |
| spellingShingle | Khiyabani, Farzin Modarres Abu Hassan, Malik Leong, Wah June Convergence of symmetric rank-one method based on modified Quasi-Newton equation |
| title | 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_short | 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 |
| url | http://psasir.upm.edu.my/id/eprint/13792/1/Convergence%20of%20symmetric%20rank.pdf |
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