Improved Hessian approximation with modified quasi-Cauchy relation for a gradient-type method
In this work we develop a new gradient-type method with improved Hessian approximation for unconstrained optimization problems. The new method resembles the Barzilai-Borwein (BB) method, except that the Hessian matrix is approximated by a diagonal matrix rather than the multiple of the identity mat...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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ICI Publishing House
2010
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| Online Access: | http://psasir.upm.edu.my/id/eprint/17711/ http://psasir.upm.edu.my/id/eprint/17711/1/Improved_Hessian_Approximation_with_Modified_Quasi-_Cauchy_Relation_for_a_Gradient-type_Method.pdf |
| _version_ | 1848843318080831488 |
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| author | Leong, Wah June Farid, Mahboubeh Abu Hassan, Malik |
| author_facet | Leong, Wah June Farid, Mahboubeh Abu Hassan, Malik |
| author_sort | Leong, Wah June |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | In this work we develop a new gradient-type method with improved Hessian approximation for unconstrained optimization problems. The new method resembles the Barzilai-Borwein (BB) method, except that the Hessian matrix is approximated by a diagonal matrix rather than the
multiple of the identity matrix in the BB method. Then the diagonal Hessian approximation is derived based on the quasi-Cauchy relation. To further improve the Hessian approximation, we modify the quasi-Cauchy relation to carry some additional information from the values and gradients of the objective function. Numerical experiments show that the proposed method yields desirable improvement. |
| first_indexed | 2025-11-15T08:13:07Z |
| format | Article |
| id | upm-17711 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T08:13:07Z |
| publishDate | 2010 |
| publisher | ICI Publishing House |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-177112019-10-09T08:17:11Z http://psasir.upm.edu.my/id/eprint/17711/ Improved Hessian approximation with modified quasi-Cauchy relation for a gradient-type method Leong, Wah June Farid, Mahboubeh Abu Hassan, Malik In this work we develop a new gradient-type method with improved Hessian approximation for unconstrained optimization problems. The new method resembles the Barzilai-Borwein (BB) method, except that the Hessian matrix is approximated by a diagonal matrix rather than the multiple of the identity matrix in the BB method. Then the diagonal Hessian approximation is derived based on the quasi-Cauchy relation. To further improve the Hessian approximation, we modify the quasi-Cauchy relation to carry some additional information from the values and gradients of the objective function. Numerical experiments show that the proposed method yields desirable improvement. ICI Publishing House 2010 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/17711/1/Improved_Hessian_Approximation_with_Modified_Quasi-_Cauchy_Relation_for_a_Gradient-type_Method.pdf Leong, Wah June and Farid, Mahboubeh and Abu Hassan, Malik (2010) Improved Hessian approximation with modified quasi-Cauchy relation for a gradient-type method. Advance Modeling and Optimization, 12 (1). pp. 37-44. ISSN 1841-4311 https://camo.ici.ro/journal/v12n1.htm |
| spellingShingle | Leong, Wah June Farid, Mahboubeh Abu Hassan, Malik Improved Hessian approximation with modified quasi-Cauchy relation for a gradient-type method |
| title | Improved Hessian approximation with modified quasi-Cauchy relation for a gradient-type method |
| title_full | Improved Hessian approximation with modified quasi-Cauchy relation for a gradient-type method |
| title_fullStr | Improved Hessian approximation with modified quasi-Cauchy relation for a gradient-type method |
| title_full_unstemmed | Improved Hessian approximation with modified quasi-Cauchy relation for a gradient-type method |
| title_short | Improved Hessian approximation with modified quasi-Cauchy relation for a gradient-type method |
| title_sort | improved hessian approximation with modified quasi-cauchy relation for a gradient-type method |
| url | http://psasir.upm.edu.my/id/eprint/17711/ http://psasir.upm.edu.my/id/eprint/17711/ http://psasir.upm.edu.my/id/eprint/17711/1/Improved_Hessian_Approximation_with_Modified_Quasi-_Cauchy_Relation_for_a_Gradient-type_Method.pdf |