The algorithms of Broyden-CG for unconstrained optimization problems
The conjugate gradient method plays an important role in solving large-scaled problems and the quasi-Newton method is known as the most efficient method in solving unconstrained optimization problems. Therefore, in this paper, the new hybrid method between the conjugate gradient method and the quasi...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Hikari
2014
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| Online Access: | http://psasir.upm.edu.my/id/eprint/5587/ http://psasir.upm.edu.my/id/eprint/5587/1/ibrahimIJMA49-52-2014.pdf |
| _version_ | 1848840141008797696 |
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| author | Ibrahim, Mohd Asrul Hery Mamat, Mustafa Leong, Wah June Mohammad Sofi, Azfi Zaidi |
| author_facet | Ibrahim, Mohd Asrul Hery Mamat, Mustafa Leong, Wah June Mohammad Sofi, Azfi Zaidi |
| author_sort | Ibrahim, Mohd Asrul Hery |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | The conjugate gradient method plays an important role in solving large-scaled problems and the quasi-Newton method is known as the most efficient method in solving unconstrained optimization problems. Therefore, in this paper, the new hybrid method between the conjugate gradient method and the quasi-newton method for solving optimization problem is suggested. The Broyden family formula is used as an approximation of Hessian in the hybrid method and the quasi-Newton method. Our numerical analysis provides strong evidence that our Broyden-CG method is more efficient than the ordinary Broyden method. Furthermore, we also prove that new algorithm is globally convergent and gratify the sufficient descent condition. |
| first_indexed | 2025-11-15T07:22:37Z |
| format | Article |
| id | upm-5587 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T07:22:37Z |
| publishDate | 2014 |
| publisher | Hikari |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-55872017-11-30T09:46:03Z http://psasir.upm.edu.my/id/eprint/5587/ The algorithms of Broyden-CG for unconstrained optimization problems Ibrahim, Mohd Asrul Hery Mamat, Mustafa Leong, Wah June Mohammad Sofi, Azfi Zaidi The conjugate gradient method plays an important role in solving large-scaled problems and the quasi-Newton method is known as the most efficient method in solving unconstrained optimization problems. Therefore, in this paper, the new hybrid method between the conjugate gradient method and the quasi-newton method for solving optimization problem is suggested. The Broyden family formula is used as an approximation of Hessian in the hybrid method and the quasi-Newton method. Our numerical analysis provides strong evidence that our Broyden-CG method is more efficient than the ordinary Broyden method. Furthermore, we also prove that new algorithm is globally convergent and gratify the sufficient descent condition. Hikari 2014 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/5587/1/ibrahimIJMA49-52-2014.pdf Ibrahim, Mohd Asrul Hery and Mamat, Mustafa and Leong, Wah June and Mohammad Sofi, Azfi Zaidi (2014) The algorithms of Broyden-CG for unconstrained optimization problems. International Journal of Mathematical Analysis, 8 (52). pp. 2591-2600. ISSN 1312-8876; ESSN: 1314-7579 http://www.m-hikari.com/ijma/ijma-2014/ijma-49-52-2014/index.html |
| spellingShingle | Ibrahim, Mohd Asrul Hery Mamat, Mustafa Leong, Wah June Mohammad Sofi, Azfi Zaidi The algorithms of Broyden-CG for unconstrained optimization problems |
| title | The algorithms of Broyden-CG for unconstrained optimization problems |
| title_full | The algorithms of Broyden-CG for unconstrained optimization problems |
| title_fullStr | The algorithms of Broyden-CG for unconstrained optimization problems |
| title_full_unstemmed | The algorithms of Broyden-CG for unconstrained optimization problems |
| title_short | The algorithms of Broyden-CG for unconstrained optimization problems |
| title_sort | algorithms of broyden-cg for unconstrained optimization problems |
| url | http://psasir.upm.edu.my/id/eprint/5587/ http://psasir.upm.edu.my/id/eprint/5587/ http://psasir.upm.edu.my/id/eprint/5587/1/ibrahimIJMA49-52-2014.pdf |