Generalized semi-infinite programming: the Symmetric Reduction Ansatz

We introduce the Symmetric Reduction Ansatz at a point from the closure of the feasible set in generalized semi-infinite programming. A corresponding Symmetric Reduction Lemma is shown for the local description of the latter set, and optimality conditions as well as topological properties are derived. We conjecture that the Symmetric Reduction Ansatz holds at all local minimizers of generic generalized semi-infinite programs.