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Scaled diagonal gradient-type method with extra update for large-scale unconstrained optimization


Farid, Mahboubeh and Leong, Wah June and Malekmohammadi, Najmeh and Mamat, Mustafa (2013) Scaled diagonal gradient-type method with extra update for large-scale unconstrained optimization. Abstract and Applied Analysis, 2013. art. no. 532041. pp. 1-5. ISSN 1085-3375; ESSN: 1687-0409


We present a new gradient method that uses scaling and extra updating within the diagonal updating for solving unconstrained optimization problem. The new method is in the frame of Barzilai and Borwein (BB) method, except that the Hessian matrix is approximated by a diagonal matrix rather than the multiple of identity matrix in the BB method. The main idea is to design a new diagonal updating scheme that incorporates scaling to instantly reduce the large eigenvalues of diagonal approximation and otherwise employs extra updates to increase small eigenvalues. These approaches give us a rapid control in the eigenvalues of the updating matrix and thus improve stepwise convergence. We show that our method is globally convergent. The effectiveness of the method is evaluated by means of numerical comparison with the BB method and its variant.

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Additional Metadata

Item Type: Article
Divisions: Faculty of Science
DOI Number: https://doi.org/10.1155/2013/532041
Publisher: Hindawi Publishing Corporation
Keywords: Large-scale optimization; Gradient method; Barzilai and Borwein method
Depositing User: Umikalthom Abdullah
Date Deposited: 23 Sep 2014 08:49
Last Modified: 19 Oct 2017 07:58
Altmetrics: http://www.altmetric.com/details.php?domain=psasir.upm.edu.my&doi=10.1155/2013/532041
URI: http://psasir.upm.edu.my/id/eprint/30321
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