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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Conditioning of quasi-Newton methods for function minimization


Author: D. F. Shanno
Journal: Math. Comp. 24 (1970), 647-656
MSC: Primary 90.58
MathSciNet review: 0274029
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Abstract: Quasi-Newton methods accelerate the steepest-descent technique for function minimization by using computational history to generate a sequence of approximations to the inverse of the Hessian matrix. This paper presents a class of approximating matrices as a function of a scalar parameter. The problem of optimal conditioning of these matrices under an appropriate norm as a function of the scalar parameter is investigated. A set of computational results verifies the superiority of the new methods arising from conditioning considerations to known methods.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1970-0274029-X
PII: S 0025-5718(1970)0274029-X
Keywords: Function minimization, quasi-Newton methods, variable metric methods, gradient search, steepest-descent methods, stability of search methods, conditioning of search methods, Hessian matrix, inverse approximations
Article copyright: © Copyright 1970 American Mathematical Society