Abstract
The authors consider Newton-like line search descent methods for solving non-linear least-squares problems. The basis of our approach is to choose a method, or parameters within a method, by minimizing a variational measure which estimates the error in an inverse Hessian approximation. In one approach we consider sizing methods and choose sizing parameters in an optimal way. In another approach we consider various possibilities for hybrid Gauss-Newton/BFGS methods. The authors conclude that a simple Gauss-Newton/BFGS hybrid is both efficient and robust and we illustrate this by a range of comparative tests with other methods. These experiments include not only many well known test problems but also some new classes of large residual problem.
| Original language | English |
|---|---|
| Pages (from-to) | 405-421 |
| Number of pages | 17 |
| Journal | Journal of the Operational Research Society |
| Volume | 36 |
| Issue number | 5 |
| Publication status | Published - May 1985 |
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ASJC Scopus subject areas
- Management of Technology and Innovation
- Strategy and Management
- Management Science and Operations Research
Cite this
VARIATIONAL METHODS FOR NON-LINEAR LEAST-SQUARES. / Al-Baali, M.; Fletcher, R.
In: Journal of the Operational Research Society, Vol. 36, No. 5, 05.1985, p. 405-421.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - VARIATIONAL METHODS FOR NON-LINEAR LEAST-SQUARES.
AU - Al-Baali, M.
AU - Fletcher, R.
PY - 1985/5
Y1 - 1985/5
N2 - The authors consider Newton-like line search descent methods for solving non-linear least-squares problems. The basis of our approach is to choose a method, or parameters within a method, by minimizing a variational measure which estimates the error in an inverse Hessian approximation. In one approach we consider sizing methods and choose sizing parameters in an optimal way. In another approach we consider various possibilities for hybrid Gauss-Newton/BFGS methods. The authors conclude that a simple Gauss-Newton/BFGS hybrid is both efficient and robust and we illustrate this by a range of comparative tests with other methods. These experiments include not only many well known test problems but also some new classes of large residual problem.
AB - The authors consider Newton-like line search descent methods for solving non-linear least-squares problems. The basis of our approach is to choose a method, or parameters within a method, by minimizing a variational measure which estimates the error in an inverse Hessian approximation. In one approach we consider sizing methods and choose sizing parameters in an optimal way. In another approach we consider various possibilities for hybrid Gauss-Newton/BFGS methods. The authors conclude that a simple Gauss-Newton/BFGS hybrid is both efficient and robust and we illustrate this by a range of comparative tests with other methods. These experiments include not only many well known test problems but also some new classes of large residual problem.
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M3 - Article
VL - 36
SP - 405
EP - 421
JO - Journal of the Operational Research Society
JF - Journal of the Operational Research Society
SN - 0160-5682
IS - 5
ER -