Matrix conditioning and nonlinear optimization View Full Text


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Article Info

DATE

1978-12

AUTHORS

D. F. Shanno, Kang -Hoh Phua

ABSTRACT

In a series of recent papers, Oren, Oren and Luenberger, Oren and Spedicato, and Spedicato have developed the self-scaling variable metric algorithms. These algorithms alter Broyden's single parameter family of approximations to the inverse Hessian to a double parameter family. Conditions are given on the new parameter to minimize a bound on the condition number of the approximated inverse Hessian while insuring improved step-wise convergence. Davidon has devised an update which also minimizes the bound on the condition number while remaining in the Broyden single parameter family. This paper derives initial scalings for the approximate inverse Hessian which makes members of the Broyden class self-scaling. The Davidon, BFGS, and Oren—Spedicato updates are tested for computational efficiency and stability on numerous test functions, with the results indicating strong superiority computationally for the Davidon and BFGS update over the self-scaling update, except on a special class of functions, the homogeneous functions. More... »

PAGES

149-160

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/bf01588962

DOI

http://dx.doi.org/10.1007/bf01588962

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1048725219


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