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Generalized Kojima–Functions and Lipschitz Stability of Critical Points

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Abstract

In this paper we consider systems of equations which are defined by nonsmooth functions of a special structure. Functions of this type are adapted from Kojima's form of the Karush–Kuhn–Tucker conditions for C2—optimization problems. We shall show that such systems often represent conditions for critical points of variational problems (nonlinear programs, complementarity problems, generalized equations, equilibrium problems and others). Our main purpose is to point out how different concepts of generalized derivatives lead to characterizations of different Lipschitz properties of the critical point or the stationary solution set maps.

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Authors and Affiliations

  1. Institut für Operations Research, Universität Zürich, CH-8044, Zürich, Switzerland

    Diethard Klatte

  2. Institut für Mathematik, Humboldt-Universität Berlin, D-10117, Berlin, Germany

    Bernd Kummer

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  1. Diethard Klatte
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  2. Bernd Kummer
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Klatte, D., Kummer, B. Generalized Kojima–Functions and Lipschitz Stability of Critical Points. Computational Optimization and Applications 13, 61–85 (1999). https://doi.org/10.1023/A:1008648605071

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