Superlinear convergence of symmetric Huang's class of methods |
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Authors: | Andrzej Stachurski |
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Institution: | (1) Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland |
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Abstract: | Summary In this paper the problem of minimizing the functionalf:DR
n
R is considered. Typical assumptions onf are assumed. A class of Quasi-Newton methods, namely Huang's class of methods is used for finding an optimal solution of this problem. A new theorem connected with this class is presented. By means of this theorem some convergence results known up till now only for the methods which satisfy Quasi-Newton condition are extended, that is the results of superlinear convergence of variable metric methods in the cases of exact and asymptotically exact minimization and the so-called direct-prediction case. This theorem allows to interpretate one of the parameters as the scaling parameter. |
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Keywords: | AMS(MOS): 65K05 CR: 5 15 |
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