Scaled Diagonal Gradient-Type Method with Extra Update for Large-Scale Unconstrained Optimization. (27th March 2013)

• Record Type: Journal Article
• Authors: Farid, Mahboubeh; Leong, Wah June; Malekmohammadi, Najmeh; Mamat, Mustafa
• Other Names: Zhou Guanglu Academic Editor.
• Is Part Of: Abstract and applied analysis. Volume 2013(2013)
• Publication Date: 2013-03-27
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/2013/532041
• Languages: English
• ISSNs: 1085-3375

Abstract

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.