Generalized Kojima–Functions and Lipschitz Stability of Critical Points

Authors:
Diethard Klatte;Bernd Kummer
Affiliations:
Institut für Operations Research, Universität Zürich, CH-8044 Zürich, Switzerlandklatte@ior.unizh.ch;Institut für Mathematik, Humboldt-Universität Berlin, D-10117 Berlin, Germanykummer@mathematik.hu-berlin.de
Venue:
Computational Optimization and Applications - Special issue on computational optimization—a tribute to Olvi Mangasarian, part II
Year:
1999

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Abstract

In this paper we consider systems of equationswhich are defined by nonsmooth functions of a specialstructure. Functions of this type are adapted fromKojima‘s form of the Karush–Kuhn–Tucker conditions forC^2—optimization problems.We shall show that such systems often represent conditionsfor critical points of variational problems(nonlinear programs, complementarity problems, generalized equations, equilibrium problems and others).Our main purpose is to point out how different conceptsof generalized derivatives lead to characterizations ofdifferent Lipschitz properties of the critical point or thestationary solution set maps.