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Subject: Parameterized generalized equation ×

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    Some remarks on stability of generalized equations
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2012) Henrion, René; Kruger, Alexander; Outrata, Jiří
    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 multi-valued term amounts to the regular normal cone to a (possibly nonconvex) set given by C2 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. On the basis of the obtained generalized derivatives, new optimality conditions for a class of mathematical programs with equilibrium constrains are derived, and a workable characterization of the isolated calmness of the considered solution map is provided.
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    On regular coderivatives in parametric equilibria with non-unique multipliers
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2012) Henrion, René; Outrata, Jiří; Surowiec, Thomas
    This paper deals with the computation of regular coderivatives of solution maps associated with a frequently arising class of generalized equations. The constraint sets are given by (not necessarily convex) inequalities, and we do not assume linear independence of gradients to active constraints. The achieved results enable us to state several versions of sharp necessary optimality conditions in optimization problems with equilibria governed by such generalized equations. The advantages are illustrated by means of examples.