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Journal of Applied Mathematics
Volume 2012, Article ID 875494, 11 pages
Research Article

Accumulative Approach in Multistep Diagonal Gradient-Type Method for Large-Scale Unconstrained Optimization

1Department of Mathematics, University Putra Malaysia, Selangor, 43400 Serdang, Malaysia
2School of Computing and Maths, Charles Sturt University, Mitchell, NSW 2795, Australia

Received 2 April 2012; Revised 10 May 2012; Accepted 16 May 2012

Academic Editor: Vu Phat

Copyright © 2012 Mahboubeh Farid et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper focuses on developing diagonal gradient-type methods that employ accumulative approach in multistep diagonal updating to determine a better Hessian approximation in each step. The interpolating curve is used to derive a generalization of the weak secant equation, which will carry the information of the local Hessian. The new parameterization of the interpolating curve in variable space is obtained by utilizing accumulative approach via a norm weighting defined by two positive definite weighting matrices. We also note that the storage needed for all computation of the proposed method is just O(n). Numerical results show that the proposed algorithm is efficient and superior by comparison with some other gradient-type methods.