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Optimization methods and stability of inclusions in Banach spaces

Klatte, Diethard ; Kummer, Bernd

In: Mathematical Programming, 2009, vol. 117, no. 1-2, p. 305-330

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    Titre
    • Optimization methods and stability of inclusions in Banach spaces
    Auteur
    • Klatte, Diethard. Institut für Operations Research, Universität Zürich, Moussonstrasse 15, CH-8044, Zürich, Switzerland
    • Kummer, Bernd. Institut für Mathematik, Humboldt-Universität zu Berlin, Unter den Linden 6, 10099, Berlin, Germany
    Type de document
    • Postprint
    Langue
    • Anglais
    Publié dans
    • Mathematical Programming, 2009, vol. 117, no. 1-2, p. 305-330. Springer-Verlag
    Autre version électronique
    Identifiant OAI-PMH
    • oai:doc.rero.ch:319114
    Summary
    Our paper deals with the interrelation of optimization methods and Lipschitz stability of multifunctions in arbitrary Banach spaces. Roughly speaking, we show that linear convergence of several first order methods and Lipschitz stability mean the same. Particularly, we characterize calmness and the Aubin property by uniformly (with respect to certain starting points) linear convergence of descent methods and approximate projection methods. So we obtain, e.g., solution methods (for solving equations or variational problems) which require calmness only. The relations of these methods to several known basic algorithms are discussed, and errors in the subroutines as well as deformations of the given mappings are permitted. We also recall how such deformations are related to standard algorithms like barrier, penalty or regularization methods in optimization