Abstract
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.
| Original language | English |
|---|---|
| Pages (from-to) | 533-553 |
| Number of pages | 21 |
| Journal | Journal of Optimization Theory and Applications |
| Volume | 96 |
| Issue number | 3 |
| Publication status | Published - Mar 1998 |
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Keywords
- Broyden family
- Global and superlinear convergence
- Inexact line searches
- Quasi-Newton methods
- Self-scaling methods
- Unconstrained optimization
ASJC Scopus subject areas
- Management Science and Operations Research
- Applied Mathematics
- Control and Optimization
Cite this
Numerical experience with a class of self-scaling quasi-newton algorithms. / Al-Baali, M.
In: Journal of Optimization Theory and Applications, Vol. 96, No. 3, 03.1998, p. 533-553.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Numerical experience with a class of self-scaling quasi-newton algorithms
AU - Al-Baali, M.
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
UR - http://www.scopus.com/inward/record.url?scp=0032373590&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0032373590&partnerID=8YFLogxK
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 -