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A class of diagonal preconditioners for limited memory BFGS method.


Leong, Wah June and Chen, Chuei Yee (2013) A class of diagonal preconditioners for limited memory BFGS method. Optimization Methods and Software, 28 (2). pp. 379-392. ISSN 1055-6788; ESSN: 1029-4937


A major weakness of the limited memory BFGS (LBFGS) method is that it may converge very slowly on ill-conditioned problems when the identity matrix is used for initialization. Very often, the LBFGS method can adopt a preconditioner on the identity matrix to speed up the convergence. For this purpose, we propose a class of diagonal preconditioners to boost the performance of the LBFGS method. In this context, we find that it is appropriate to use a diagonal preconditioner, in the form of a diagonal matrix plus a positive multiple of the identity matrix, so as to fit information of local Hessian as well as to induce positive definiteness for the diagonal preconditioner at a whole. The property of hereditary positive definiteness is maintained by a careful choice of the positive scalar on the scaled identity matrix while the local curvature information is carried implicitly on the other diagonal matrix through the variational techniques, commonly employed in the derivation of quasi-Newton updates. Several preconditioning formulae are then derived and tested on a large set of standard test problems to access the impact of different choices of such preconditioners on the minimization performance.

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Additional Metadata

Item Type: Article
Divisions: Faculty of Science
DOI Number: https://doi.org/10.1080/10556788.2011.653356
Publisher: Taylor & Francis
Keywords: Diagonal updating; Large-scale optimization; Limited memory BFGS method; Preconditioning; Weak-quasi-Newton equation.
Depositing User: Umikalthom Abdullah
Date Deposited: 30 May 2014 01:39
Last Modified: 01 Oct 2015 23:38
Altmetrics: http://www.altmetric.com/details.php?domain=psasir.upm.edu.my&doi=10.1080/10556788.2011.653356
URI: http://psasir.upm.edu.my/id/eprint/29993
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