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...

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Main Authors: Ibrahim, Mohd Asrul Hery, Mamat, Mustafa, Leong, Wah June, Mohammad Sofi, Azfi Zaidi
Format: Article
Language:English
Published: Hikari 2014
Online Access:http://psasir.upm.edu.my/id/eprint/5587/
http://psasir.upm.edu.my/id/eprint/5587/1/ibrahimIJMA49-52-2014.pdf
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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.
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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