Abstract
A new method is presented using inclusive functions and interval arithmetic for bounding the level sets of nonlinear parameter estimation problems with objective function of sum-of-squares type. The result box bounding a level set conveys more information for the user than the usual local minimum points do. The rate of convergence is in general linear, in special cases it can be superlinear or higher. The condition of convergence is studied, and examples are shown.
Zusammenfassung
Es wird eine neue Methode vorgestellt für die Beschränkung der Niveaumengen von nichtlinearen Parameterschätzungsaufgaben mit Zielfunktion von Quadratsummen-Form unter Verwendung von Inklusionsfunktionen und Intervallarithmetik. Die Ergebnismenge, die eine Niveaumenge beschränkt, bietet mehr Informationen für den Benutzer als die üblichen lokalen Minimum-Punkte. Die Konvergenzgeschwindigkeit ist im allgemeinen linear, in Spezialfällen kann sie superlinear oder höher sein. Die Konvergenzbedingungen werden untersucht und Beispiele gezeigt.
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Csendes, T. An interval method for bounding level sets of parameter estimation problems. Computing 41, 75–86 (1989). https://doi.org/10.1007/BF02238730
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DOI: https://doi.org/10.1007/BF02238730