Abstract
In this paper a method is described for solving linearly constrained nonlinear programming problems without evaluating any derivatives of the objective function. The algorithm uses the concept of active constraints and avoids the calculation of derivatives by approximating modified gradients and Hessian matrices by the aid of differences of function values. These approximations are calculated in such a way that the same convergence results are obtained as for any Quasi-Newton method.
Zusammenfassung
Es wird ein Verfahren beschrieben, das nichtlineare Optimierungsprobleme mit linearen Nebenbedingungen löst, ohne daß Ableitungen der Zielfunktion berechnet werden müssen. Der Algorithmus verwendet das Konzept der aktiven Nebenbedingungen und vermeidet die Berechnung von Ableitungen, indem modifizierte Gradienten und Hessesche Matrizen mit Hilfe von Funktionswertdifferenzen approximiert werden. Diese Approximationen werden so berechnet, daß man dieselben Konvergenzergebnisse erhält wie für jede Quasi-Newton-Methode.
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Bräuninger, J. A quasi-Newton method for minimization under linear constraints without evaluating any derivatives. Computing 21, 127–141 (1979). https://doi.org/10.1007/BF02253133
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DOI: https://doi.org/10.1007/BF02253133