Scaled Diagonal Gradient-Type Method with Extra Update for Large-Scale Unconstrained Optimization
We present a new gradient method that uses scaling and extra updating within the diagonal updating for solving unconstrained optimization problem. The new method is in the frame of Barzilai and Borwein (BB) method, except that the Hessian matrix is approximated by a diagonal matrix rather than the m...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/532041 |
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| _version_ | 1832545865643851776 |
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| author | Mahboubeh Farid Wah June Leong Najmeh Malekmohammadi Mustafa Mamat |
| author_facet | Mahboubeh Farid Wah June Leong Najmeh Malekmohammadi Mustafa Mamat |
| author_sort | Mahboubeh Farid |
| collection | DOAJ |
| description | We present a new gradient method that uses scaling and extra updating within the diagonal updating for solving unconstrained optimization problem. The new method is in the frame of Barzilai and Borwein (BB) method, except that the Hessian matrix is approximated by a diagonal matrix rather than the multiple of identity matrix in the BB method. The main idea is to design a new diagonal updating scheme that incorporates scaling to instantly reduce the large eigenvalues of diagonal approximation and otherwise employs extra updates to increase small eigenvalues. These approaches give us a rapid control in the eigenvalues of the updating matrix and thus improve stepwise convergence. We show that our method is globally convergent. The effectiveness of the method is evaluated by means of numerical comparison with the BB method and its variant. |
| format | Article |
| id | doaj-art-85e6657bc29c429abbf82294a5f9930f |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-85e6657bc29c429abbf82294a5f9930f2025-02-03T07:24:30ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/532041532041Scaled Diagonal Gradient-Type Method with Extra Update for Large-Scale Unconstrained OptimizationMahboubeh Farid0Wah June Leong1Najmeh Malekmohammadi2Mustafa Mamat3Department of Mathematics, University Putra Malaysia, 43400 Serdang, Selangor, MalaysiaDepartment of Mathematics, University Putra Malaysia, 43400 Serdang, Selangor, MalaysiaDepartment of Mathematics, Islamic Azad University, South Tehran Branch, Tehran 1418765663, IranDepartment of Mathematics, Faculty of Science and Technology, University Malaysia Terengganu, 21030 Kuala Terengganu, MalaysiaWe present a new gradient method that uses scaling and extra updating within the diagonal updating for solving unconstrained optimization problem. The new method is in the frame of Barzilai and Borwein (BB) method, except that the Hessian matrix is approximated by a diagonal matrix rather than the multiple of identity matrix in the BB method. The main idea is to design a new diagonal updating scheme that incorporates scaling to instantly reduce the large eigenvalues of diagonal approximation and otherwise employs extra updates to increase small eigenvalues. These approaches give us a rapid control in the eigenvalues of the updating matrix and thus improve stepwise convergence. We show that our method is globally convergent. The effectiveness of the method is evaluated by means of numerical comparison with the BB method and its variant.http://dx.doi.org/10.1155/2013/532041 |
| spellingShingle | Mahboubeh Farid Wah June Leong Najmeh Malekmohammadi Mustafa Mamat Scaled Diagonal Gradient-Type Method with Extra Update for Large-Scale Unconstrained Optimization Abstract and Applied Analysis |
| title | Scaled Diagonal Gradient-Type Method with Extra Update for Large-Scale Unconstrained Optimization |
| title_full | Scaled Diagonal Gradient-Type Method with Extra Update for Large-Scale Unconstrained Optimization |
| title_fullStr | Scaled Diagonal Gradient-Type Method with Extra Update for Large-Scale Unconstrained Optimization |
| title_full_unstemmed | Scaled Diagonal Gradient-Type Method with Extra Update for Large-Scale Unconstrained Optimization |
| title_short | Scaled Diagonal Gradient-Type Method with Extra Update for Large-Scale Unconstrained Optimization |
| title_sort | scaled diagonal gradient type method with extra update for large scale unconstrained optimization |
| url | http://dx.doi.org/10.1155/2013/532041 |
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