Abstract
Davidon has recently introduced a new approach to optimization using the idea of nonlinear scaling. In this paper we study the algorithm that results when applying his ideas to the one-dimensional case. We show that the algorithm is locally convergent withQ-order equal 2 and compare it with the method of cubic interpolation.
Zusammenfassung
Kürzlich wurde von Davidon für Optimierungsprobleme ein neuer Weg vorgeschlagen, bei dem die Idee der nichtlinearen Skalierung verwendet wird. Der Algorithmus wird in der vorliegenden Arbeit analysiert für den eindimensionalen Fall. Es wird gezeigt, daß der Algorithmus lokal konvergiert mit quadratischerQ-Konvergenz und die Konvergenzeigenschaften werden mit denjenigen der Methode der kubischen Interpolation verglichen.
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Supported by the Norwegian Research Council for Science and the Humanities and in part by the U.S. Army Research Grant No. DAHCO4-75-G-0185.
Supported by the Universidad Nacional Autonoma de Mexico and Banco de Mexico.
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Bjørstad, P., Nocedal, J. Analysis of a new algorithm for one-dimensional minimization. Computing 22, 93–100 (1979). https://doi.org/10.1007/BF02246561
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DOI: https://doi.org/10.1007/BF02246561