ISSN:
1436-4646
Keywords:
Quasi-Newton updates
;
convergence theory
Source:
Springer Online Journal Archives 1860-2000
Topics:
Computer Science
,
Mathematics
Notes:
Abstract Quasi-Newton algorithms for unconstrained nonlinear minimization generate a sequence of matrices that can be considered as approximations of the objective function second derivatives. This paper gives conditions under which these approximations can be proved to converge globally to the true Hessian matrix, in the case where the Symmetric Rank One update formula is used. The rate of convergence is also examined and proven to be improving with the rate of convergence of the underlying iterates. The theory is confirmed by some numerical experiments that also show the convergence of the Hessian approximations to be substantially slower for other known quasi-Newton formulae.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01594934
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