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General semi-infinite optimization problems arise in a number of real-life applications and can often be solved by a numerical method which exploits the inherent bi-level structure of GSIP. In this work we have seen that strong optimality conditions for GSIP can only be formulated after a sound understanding of the topology of its feasible set. As numerical methods can in general only be expected to converge to a stationary point of GSIP, optimality conditions serve the important purpose to define the appropriate concept of stationarity.
KeywordsConstraint Qualification Order Optimality Condition Generalize Critical Point Finite Dimensional Optimization Problem Abadie Constraint Qualification
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