Accumulative Approach in Multistep Diagonal Gradient-Type Method for Large-Scale Unconstrained Optimization
This paper focuses on developing diagonal gradient-type methods that employ accumulative approach in multistep diagonal updating to determine a better Hessian approximation in each step. The interpolating curve is used to derive a generalization of the weak secant equation, which will carry the info...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/875494 |
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| _version_ | 1850160367518351360 |
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| author | Mahboubeh Farid Wah June Leong Lihong Zheng |
| author_facet | Mahboubeh Farid Wah June Leong Lihong Zheng |
| author_sort | Mahboubeh Farid |
| collection | DOAJ |
| description | This paper focuses on developing diagonal gradient-type methods that employ accumulative approach in multistep diagonal updating to determine a better Hessian approximation in each step. The interpolating curve is used to derive a generalization of the weak secant equation, which will carry the information of the local Hessian. The new parameterization of the interpolating curve in variable space is obtained by utilizing accumulative approach via a norm weighting defined by two positive definite weighting matrices. We also note that the storage needed for all computation of the proposed method is just O(n). Numerical results show that the proposed algorithm is efficient and superior by comparison with some other gradient-type methods. |
| format | Article |
| id | doaj-art-b6ff178ac0a446a9be0d0bc8c0fbd3ea |
| institution | OA Journals |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-b6ff178ac0a446a9be0d0bc8c0fbd3ea2025-08-20T02:23:09ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/875494875494Accumulative Approach in Multistep Diagonal Gradient-Type Method for Large-Scale Unconstrained OptimizationMahboubeh Farid0Wah June Leong1Lihong Zheng2Department of Mathematics, University Putra Malaysia, Selangor, 43400 Serdang, MalaysiaDepartment of Mathematics, University Putra Malaysia, Selangor, 43400 Serdang, MalaysiaSchool of Computing and Maths, Charles Sturt University, Mitchell, NSW 2795, AustraliaThis paper focuses on developing diagonal gradient-type methods that employ accumulative approach in multistep diagonal updating to determine a better Hessian approximation in each step. The interpolating curve is used to derive a generalization of the weak secant equation, which will carry the information of the local Hessian. The new parameterization of the interpolating curve in variable space is obtained by utilizing accumulative approach via a norm weighting defined by two positive definite weighting matrices. We also note that the storage needed for all computation of the proposed method is just O(n). Numerical results show that the proposed algorithm is efficient and superior by comparison with some other gradient-type methods.http://dx.doi.org/10.1155/2012/875494 |
| spellingShingle | Mahboubeh Farid Wah June Leong Lihong Zheng Accumulative Approach in Multistep Diagonal Gradient-Type Method for Large-Scale Unconstrained Optimization Journal of Applied Mathematics |
| title | Accumulative Approach in Multistep Diagonal Gradient-Type Method for Large-Scale Unconstrained Optimization |
| title_full | Accumulative Approach in Multistep Diagonal Gradient-Type Method for Large-Scale Unconstrained Optimization |
| title_fullStr | Accumulative Approach in Multistep Diagonal Gradient-Type Method for Large-Scale Unconstrained Optimization |
| title_full_unstemmed | Accumulative Approach in Multistep Diagonal Gradient-Type Method for Large-Scale Unconstrained Optimization |
| title_short | Accumulative Approach in Multistep Diagonal Gradient-Type Method for Large-Scale Unconstrained Optimization |
| title_sort | accumulative approach in multistep diagonal gradient type method for large scale unconstrained optimization |
| url | http://dx.doi.org/10.1155/2012/875494 |
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