A new gradient method via quasi-Cauchy relation which guarantees descent
We propose a new monotone algorithm for unconstrained optimization in the frame of Barzilai and Borwein (BB) method and analyze the convergence properties of this new descent method. Motivated by the fact that BB method does not guarantee descent in the objective function at each iteration, but perf...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Elsevier BV
2009
|
| Online Access: | http://psasir.upm.edu.my/id/eprint/12747/ http://psasir.upm.edu.my/id/eprint/12747/1/A%20new%20gradient%20method%20via%20quasi.pdf |
| _version_ | 1848841919678906368 |
|---|---|
| author | Abu Hassan, Malik Leong, Wah June Farid, Mahboubeh |
| author_facet | Abu Hassan, Malik Leong, Wah June Farid, Mahboubeh |
| author_sort | Abu Hassan, Malik |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | We propose a new monotone algorithm for unconstrained optimization in the frame of Barzilai and Borwein (BB) method and analyze the convergence properties of this new descent method. Motivated by the fact that BB method does not guarantee descent in the objective function at each iteration, but performs better than the steepest descent method, we therefore attempt to find stepsize formula which enables us to approximate the Hessian based on the Quasi-Cauchy equation and possess monotone property in each iteration. Practical insights on the effectiveness of the proposed techniques are given by a numerical comparison with the BB method. |
| first_indexed | 2025-11-15T07:50:53Z |
| format | Article |
| id | upm-12747 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T07:50:53Z |
| publishDate | 2009 |
| publisher | Elsevier BV |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-127472015-11-13T03:44:24Z http://psasir.upm.edu.my/id/eprint/12747/ A new gradient method via quasi-Cauchy relation which guarantees descent Abu Hassan, Malik Leong, Wah June Farid, Mahboubeh We propose a new monotone algorithm for unconstrained optimization in the frame of Barzilai and Borwein (BB) method and analyze the convergence properties of this new descent method. Motivated by the fact that BB method does not guarantee descent in the objective function at each iteration, but performs better than the steepest descent method, we therefore attempt to find stepsize formula which enables us to approximate the Hessian based on the Quasi-Cauchy equation and possess monotone property in each iteration. Practical insights on the effectiveness of the proposed techniques are given by a numerical comparison with the BB method. Elsevier BV 2009-08-01 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/12747/1/A%20new%20gradient%20method%20via%20quasi.pdf Abu Hassan, Malik and Leong, Wah June and Farid, Mahboubeh (2009) A new gradient method via quasi-Cauchy relation which guarantees descent. Journal of Computational and Applied Mathematics, 230 (1). pp. 300-305. ISSN 0377-0427; ESSN: 1879-1778 10.1016/j.cam.2008.11.013 |
| spellingShingle | Abu Hassan, Malik Leong, Wah June Farid, Mahboubeh A new gradient method via quasi-Cauchy relation which guarantees descent |
| title | A new gradient method via quasi-Cauchy relation which guarantees descent |
| title_full | A new gradient method via quasi-Cauchy relation which guarantees descent |
| title_fullStr | A new gradient method via quasi-Cauchy relation which guarantees descent |
| title_full_unstemmed | A new gradient method via quasi-Cauchy relation which guarantees descent |
| title_short | A new gradient method via quasi-Cauchy relation which guarantees descent |
| title_sort | new gradient method via quasi-cauchy relation which guarantees descent |
| url | http://psasir.upm.edu.my/id/eprint/12747/ http://psasir.upm.edu.my/id/eprint/12747/ http://psasir.upm.edu.my/id/eprint/12747/1/A%20new%20gradient%20method%20via%20quasi.pdf |