New implicit multistep quasi-Newton methods
- 1 April 2009
- journal article
- Published by Pleiades Publishing Ltd in Numerical Analysis and Applications
- Vol. 2 (2) , 154-164
Abstract
Multistep quasi-Newton optimization methods use data from more than one previous step to construct the current Hessian approximation. These methods were introduced in [3, 4] where it is shown how to construct such methods by means of interpolating curves. To obtain a better parametrization of the interpolation, Ford [2] developed the idea of “implicit” methods. In this paper, we describe a derivation of new implicit updates which are similar to methods I4 and I5 created in [17]. The experimental results presented here show that both of the new methods produce better performance than the existing methods, especially as the dimension of the test problem grows.Keywords
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