Nonmonotone trust region methods with curvilinear path in unconstrained optimization

A general nonmonotone trust region method with curvilinear path for unconstrained optimization problem is presented. Although this method allows the sequence of the objective function values to be nonmonotone, convergence properties similar to those for the usual trust region methods with curvilinear path are proved under certain conditions. Some numerical results are reported which show the superiority of the nonmonotone trust region method with respect to the numbers of gradient evaluations and function evaluations.ZusammenfassungEs wird ein allgemeines nichtmonotones Konfidenzbereichs-Verfahren mit krummlinigem Pfad für die unrestringierte Optimierung vorgeschlagen. Obwohl bei diesem Verfahren die Folge der Werte der Objecktfunktion nicht monoton zu sein braucht, werden Konvergenzeigenschaften bewiesen, die denen der gängigen Verfahren dieser Art entsprechen. An Hand einiger numerischer Beispiele wird die Über-legenheit des nichtmonotonen Verfahrens bezüglich der Zahl der Gradienten- und der Funktions-auswertungen gezeigt.

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