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2013 Scaled Diagonal Gradient-Type Method with Extra Update for Large-Scale Unconstrained Optimization
Mahboubeh Farid, Wah June Leong, Najmeh Malekmohammadi, Mustafa Mamat
Abstr. Appl. Anal. 2013(SI23): 1-5 (2013). DOI: 10.1155/2013/532041


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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Mahboubeh Farid. Wah June Leong. Najmeh Malekmohammadi. Mustafa Mamat. "Scaled Diagonal Gradient-Type Method with Extra Update for Large-Scale Unconstrained Optimization." Abstr. Appl. Anal. 2013 (SI23) 1 - 5, 2013.


Published: 2013
First available in Project Euclid: 26 February 2014

zbMATH: 1384.90121
MathSciNet: MR3039128
Digital Object Identifier: 10.1155/2013/532041

Rights: Copyright © 2013 Hindawi

Vol.2013 • No. SI23 • 2013
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