Some Remarks on Stability of Generalized Equations |
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Authors: | René Henrion Alexander Y Kruger Ji?í V Outrata |
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Institution: | 1. Weierstrass Institute for Applied Analysis and Stochastics, 10117, Berlin, Germany 2. Centre for Informatics and Applied Optimization, School of Science, Information Technology and Engineering, University of Ballarat, POB 663, Ballarat, Vic, 3350, Australia 3. Institute of Information Theory and Automation, Academy of Sciences of the Czech Republic, 18208, Prague, Czech Republic
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Abstract: | The paper concerns the computation of the graphical derivative and the regular (Fréchet) coderivative of the solution map to a class of generalized equations, where the multivalued term amounts to the regular normal cone to a (possibly nonconvex) set given by C 2 inequalities. Instead of the linear independence qualification condition, standardly used in this context, one assumes a combination of the Mangasarian–Fromovitz and the constant rank qualification conditions. Based on the obtained generalized derivatives, new optimality conditions for a class of mathematical programs with equilibrium constraints are derived, and a workable characterization of the isolated calmness of the considered solution map is provided. |
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