Electronic Resource
Springer
Journal of optimization theory and applications
33 (1981), S. 311-324
ISSN:
1573-2878
Keywords:
Broyden methods
;
quasi-Newton methods
;
degenerate values
;
Dixon's theorem
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract A Broyden method fails when the free parameter φ takes on a degenerate value; one such value is well known, but this paper shows that many others exist in general. These values have practical significance if the initial Hessian approximation is indefinite. The BFS formula is special in that it avoids these degenerate values. Properties about how the new degenerate values behave and their relationship to the well-known degenerate value are described. A new result is used about a reduced inverse Hessian method, which is equivalent to a Broyden method but is parameter free and provides a simple proof of Dixon's theorem.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00935247
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