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...

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Main Authors: Leong, Wah June, Farid, Mahboubeh, Abu Hassan, Malik
Format: Article
Language:English
Published: ICI Publishing House 2010
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
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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.
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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