Abstract
Two basic approaches to the generation of conjugate directions are considered for the problem of unconstrained minimisation of quadratic functions. The first approach results in a projected gradient algorithm which gives 'n step' convergence for a quadratic. The second approach is based on the generalised solution of a set of underdetermined linear equations, various forms of which generate various new algorithms also giving n step convergence. One of them is the Fletcher and Powell modification of Davidon's method. Results of an extensive numerical comparison of these methods with the Newton–Raphson method, the Fletcher–Reeves method, and the Fletcher–Powell–Davidon method are included, the test functions being non-quadratic.
Keywords
Minimisation (clinical trials)MathematicsUnderdetermined systemQuadratic equationConjugate gradient methodApplied mathematicsQuadratic functionMathematical optimizationAlgorithmComputer science
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Publication Info
- Year
- 1969
- Type
- article
- Volume
- 12
- Issue
- 2
- Pages
- 171-178
- Citations
- 143
- Access
- Closed
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Cite This
J. Pearson
(1969).
Variable metric methods of minimisation.
The Computer Journal
, 12
(2)
, 171-178.
https://doi.org/10.1093/comjnl/12.2.171
Identifiers
- DOI
- 10.1093/comjnl/12.2.171