Abstract
The paper deals with the feasible setM of a semi-infinite optimization problem, i.e.M is a subset of the finite-dimensional Euclidean space and is basically defined by infinitely many inequality constraints. Assuming that the extended Mangasarian-Fromovitz constraint qualification holds at all points fromM, it is shown that the quadratic distance function with respect toM is continuously differentiable on an open neighborhood ofM. If, in addition,M is compact, then the set $$\tilde M$$ , which is described by this quadratic distance function, is shown to be an appropriate approximation ofM and the setsM and $$\tilde M$$ can be topologically identified via a homeomorphism.
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