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Generalized Kojima-functions and Lipschitz stability of critical points. (English) Zbl 1017.90104

Summary: In this paper we consider systems of equations which are defined by nonsmooth functions of a special structure. Functions of this type from Kojima’s form of the Karush-Kuhn-Tucker conditions for \(C^2\)-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 of the stationary solution set maps.

MSC:

90C30 Nonlinear programming
90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
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