TY - JOUR
T1 - Numerical experience with a class of self-scaling quasi-newton algorithms
AU - Al-Baali, M.
N1 - Funding Information:
1An early version was presented at the 4th SIAM Conference on Optimization, Chicago, Illinois, 1992. 2is research was supported in part by a grant from the Italian Ministry of University. The author is indebted to Lucio Grandinetti for stimulating discussions. He thanks an anonymous referee, Robert B. Schnabel, and Humaid Khalfan for valuable comments on the draft of this paper. 3Head, Department of Mathematics and Computer Science, Faculty of Science, UAE University, Al-Ain, United Arab Emirates; on leave from the Department of Mathematics, Faculty of Science, University of Damascus, Damascus, Syria.
PY - 1998/3
Y1 - 1998/3
N2 - Self-scaling quasi-Newton methods for unconstrained optimization depend upon updating the Hessian approximation by a formula which depends on two parameters (say, τ and θ) such that τ = 1, θ = 0, and θ = 1 yield the unscaled Broyden family, the BFGS update, and the DFP update, respectively. In previous work, conditions were obtained on these parameters that imply global and superlinear convergence for self-scaling methods on convex objective functions. This paper discusses the practical performance of several new algorithms designed to satisfy these conditions.
AB - Self-scaling quasi-Newton methods for unconstrained optimization depend upon updating the Hessian approximation by a formula which depends on two parameters (say, τ and θ) such that τ = 1, θ = 0, and θ = 1 yield the unscaled Broyden family, the BFGS update, and the DFP update, respectively. In previous work, conditions were obtained on these parameters that imply global and superlinear convergence for self-scaling methods on convex objective functions. This paper discusses the practical performance of several new algorithms designed to satisfy these conditions.
KW - Broyden family
KW - Global and superlinear convergence
KW - Inexact line searches
KW - Quasi-Newton methods
KW - Self-scaling methods
KW - Unconstrained optimization
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U2 - 10.1023/A:1022608410710
DO - 10.1023/A:1022608410710
M3 - Article
AN - SCOPUS:0032373590
VL - 96
SP - 533
EP - 553
JO - Journal of Optimization Theory and Applications
JF - Journal of Optimization Theory and Applications
SN - 0022-3239
IS - 3
ER -