Self-Scaling Variable Metric (SSVM) Algorithms
A new criterion is introduced for comparing the convergence properties of variable metric algorithms, focusing on stepwise descent properties. This criterion is a bound on the rate of decrease in the function value at each iterative step (single-step convergence rate). Using this criterion as a basis for algorithm development leads to the introduction of variable coefficients to rescale the objective function at each iteration, and, correspondingly, to a new class of variable metric algorithms. Effective scaling can be implemented by restricting the parameters in a two-parameter family of variable metric algorithms. Conditions are derived for these parameters that guarantee monotonic improvement in the single-step convergence rate. These conditions are obtained by analyzing the eigenvalue structure of the associated inverse Hessian approximations.
Year of publication: |
1974
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Authors: | Oren, Shmuel S. ; Luenberger, David G. |
Published in: |
Management Science. - Institute for Operations Research and the Management Sciences - INFORMS, ISSN 0025-1909. - Vol. 20.1974, 5, p. 845-862
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Publisher: |
Institute for Operations Research and the Management Sciences - INFORMS |
Saved in:
Online Resource
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