The CG-BFGS method for unconstrained optimization problems
In this paper we present a new search direction known as the CG-BFGS method, which uses the search direction of the conjugate gradient method approach in the quasi-Newton methods. The new algorithm is compared with the quasi-Newton methods in terms of the number of iterations and CPU-time. The Broyd...
| Main Authors: | , , , |
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| Format: | Conference or Workshop Item |
| Language: | English |
| Published: |
AIP Publishing LLC
2013
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| Online Access: | http://psasir.upm.edu.my/id/eprint/36856/ http://psasir.upm.edu.my/id/eprint/36856/1/The%20CG-BFGS%20method%20for%20unconstrained%20optimization%20problems.pdf |
| _version_ | 1848848449450016768 |
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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 | In this paper we present a new search direction known as the CG-BFGS method, which uses the search direction of the conjugate gradient method approach in the quasi-Newton methods. The new algorithm is compared with the quasi-Newton methods in terms of the number of iterations and CPU-time. The Broyden-Fletcher-Goldfarb-Shanno (BFGS) method is used as an updating formula for the approximation of the Hessian for both methods. Our numerical analysis provides strong evidence that our CG-BFGS method is more efficient than the ordinary BFGS method. Besides, we also prove that the new algorithm is globally convergent. |
| first_indexed | 2025-11-15T09:34:41Z |
| format | Conference or Workshop Item |
| id | upm-36856 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T09:34:41Z |
| publishDate | 2013 |
| publisher | AIP Publishing LLC |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-368562017-09-28T02:01:14Z http://psasir.upm.edu.my/id/eprint/36856/ The CG-BFGS method for unconstrained optimization problems Ibrahim, Mohd Asrul Hery Mamat, Mustafa Leong, Wah June Mohammad Sofi, Azfi Zaidi In this paper we present a new search direction known as the CG-BFGS method, which uses the search direction of the conjugate gradient method approach in the quasi-Newton methods. The new algorithm is compared with the quasi-Newton methods in terms of the number of iterations and CPU-time. The Broyden-Fletcher-Goldfarb-Shanno (BFGS) method is used as an updating formula for the approximation of the Hessian for both methods. Our numerical analysis provides strong evidence that our CG-BFGS method is more efficient than the ordinary BFGS method. Besides, we also prove that the new algorithm is globally convergent. AIP Publishing LLC 2013 Conference or Workshop Item PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/36856/1/The%20CG-BFGS%20method%20for%20unconstrained%20optimization%20problems.pdf Ibrahim, Mohd Asrul Hery and Mamat, Mustafa and Leong, Wah June and Mohammad Sofi, Azfi Zaidi (2013) The CG-BFGS method for unconstrained optimization problems. In: 21st National Symposium on Mathematical Sciences (SKSM21), 6-8 Nov. 2013, Penang, Malaysia. (pp. 167-172). 10.1063/1.4887583 |
| spellingShingle | Ibrahim, Mohd Asrul Hery Mamat, Mustafa Leong, Wah June Mohammad Sofi, Azfi Zaidi The CG-BFGS method for unconstrained optimization problems |
| title | The CG-BFGS method for unconstrained optimization problems |
| title_full | The CG-BFGS method for unconstrained optimization problems |
| title_fullStr | The CG-BFGS method for unconstrained optimization problems |
| title_full_unstemmed | The CG-BFGS method for unconstrained optimization problems |
| title_short | The CG-BFGS method for unconstrained optimization problems |
| title_sort | cg-bfgs method for unconstrained optimization problems |
| url | http://psasir.upm.edu.my/id/eprint/36856/ http://psasir.upm.edu.my/id/eprint/36856/ http://psasir.upm.edu.my/id/eprint/36856/1/The%20CG-BFGS%20method%20for%20unconstrained%20optimization%20problems.pdf |