Abstract
An approach to variable metric algorithms has been investigated in which the linear search sub-problem no longer becomes necessary. The property of quadratic termination has been replaced by one of monotonic convergence of the eigenvalues of the approximating matrix to the inverse hessian. A convex class of updating formulae which possess this property has been established, and a strategy has been indicated for choosing a member of the class so as to keep the approximation away from both singularity and unboundedness. A FORTRAN program has been tested extensively with encouraging results.
Keywords
Hessian matrixMonotonic functionEigenvalues and eigenvectorsMetric (unit)Variable (mathematics)FortranClass (philosophy)InverseProperty (philosophy)MathematicsConvergence (economics)AlgorithmApplied mathematicsQuadratic equationMatrix (chemical analysis)Mathematical optimizationComputer scienceMathematical analysisGeometry
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Publication Info
- Year
- 1970
- Type
- article
- Volume
- 13
- Issue
- 3
- Pages
- 317-322
- Citations
- 3951
- Access
- Closed
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Cite This
R. Fletcher
(1970).
A new approach to variable metric algorithms.
The Computer Journal
, 13
(3)
, 317-322.
https://doi.org/10.1093/comjnl/13.3.317
Identifiers
- DOI
- 10.1093/comjnl/13.3.317