Abstract
This tutorial paper deals with feasible sets of semi-infinite optimization problems (SIP) which are defined by finitely many equality and infinitely many inequality constraints, where all appearing functions are real-valued and defined on ℝ n . Many practical tasks lead to problems of the type (SIP), e.g. in robotics, design centering, Chebyshev approximation, etc. An overview is given about results concerning the close relationship between the overall validity of an appropriate constraint qualification of the Mangasarian-Fromovitz type and certain global topological stability properties of the (noncompact) feasible set of (SIP), where perturbations in the function space with respect to the strong (or Whitney-) C 1 topology as well as variations of an additional real parameter are considered. In particular, several basic geometric ideas of the proofs of the mentioned results are presented.
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