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Stephan Dempe (dempemath.tufreiberg.de) Abstract: This paper contributes to a deeper understanding of the link between a now conventional framework in hierarchical optimization spread under the name of the optimistic bilevel problem and its initial more dicult formulation that we call here the original optimistic bilevel optimization problem. It follows from this research that, although the process of deriving necessary optimality conditions for the latter problem is more involved, the conditions themselves do notto a large extentdiffer from those known for the conventional problem. It has been already well recognized in the literature that for optimality conditions of the usual optimistic bilevel program appropriate coderivative constructions for the setvalued solution map of the lowerlevel problem could be used, while it is shown in this paper that for the original optimistic formulation we have to go a step further to require and justify a certain Lipschitzlike property of this map. This occurs to be related to the local Lipschitz continuity of the optimal value function of an optimization problem constrained by solutions to another optimization problem; this function is labeled here as the two level value function. More generally, we conduct a detailed sensitivity analysis for value functions of mathematical programs with extended complementarity constraints. The results obtained in this vein are applied to the twolevel value function and then to the original optimistic formulation of the bilevel optimization problem, for which we derive veriable stationarity conditions of various types entirely in terms of the initial data. Keywords: Bilevel programming, Coderivative, Lipschitzlike property, Sensitivity analysis, Twolevel value function, MPCC value functions, Optimality conditions Category 1: Convex and Nonsmooth Optimization (Nonsmooth Optimization ) Category 2: Nonlinear Optimization Category 3: Nonlinear Optimization (Unconstrained Optimization ) Citation: Preprint 201107, Department of Mathematics and Computer Science, Technical University Bergakademie Freiberg, Freiberg, Germany, October 2011 Download: [PDF] Entry Submitted: 11/03/2011 Modify/Update this entry  
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