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The feasible set in generalized semi-infinite optimization

Oliver Stein

Abstract. This article gives a brief survey about recent results in generalized semi-infinite optimization. We are mainly concerned with the structure of feasible sets, since a thorough understanding of their topological features lays the groundwork for strong optimality conditions. We give descriptions of feasible sets from three different perspectives.

The appearance of stable re-entrant corner points and local non-closedness is motivated by a projection formula and elaborated for a linear case as well as for the non-linear case of so-called mai-points. A sufficient condition for closedness of the feasible set is given via a set-valued mapping formula. From the description of the feasible set by an optimal value function we derive topological properties as well as estimates for first order tangent cones. The latter estimates eventually give rise to first order optimality conditions.