Abstract and Applied Analysis

Scaled Diagonal Gradient-Type Method with Extra Update for Large-Scale Unconstrained Optimization

Mahboubeh Farid, Wah June Leong, Najmeh Malekmohammadi, and Mustafa Mamat

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Abstract

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.

Article information

Source
Abstr. Appl. Anal., Volume 2013, Special Issue (2012), Article ID 532041, 5 pages.

Dates
First available in Project Euclid: 26 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1393450468

Digital Object Identifier
doi:10.1155/2013/532041

Mathematical Reviews number (MathSciNet)
MR3039128

Zentralblatt MATH identifier
1384.90121

Citation

Farid, Mahboubeh; Leong, Wah June; Malekmohammadi, Najmeh; Mamat, Mustafa. Scaled Diagonal Gradient-Type Method with Extra Update for Large-Scale Unconstrained Optimization. Abstr. Appl. Anal. 2013, Special Issue (2012), Article ID 532041, 5 pages. doi:10.1155/2013/532041. https://projecteuclid.org/euclid.aaa/1393450468


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