Generalized Semi-Infinite Programming: The Nonsmooth Symmetric Reduction Ansatz

The feasible set M in generalized semi-infinite programming (GSIP) need not be closed. Under the so-called symmetric Mangasarian-Fromovitz constraint qualification (Sym- MFCQ), its closure ... can be described by means of infinitely many inequality constraints of maximum type. This paper introduces the nonsmooth symmetric reduction ansatz (NSRA). Under NSRA the paper proves that the set ... can locally be described as the feasible set of a so-called disjunctive optimization problem defined by finitely many inequality constraints of maximum type. Under Sym-MFCQ all local minimizers of GSIP are KKT points for GSIP. The paper shows that NSRA is generic and stable at all KKT points and that all KKT points are nondegenerate. The concept of (nondegenerate) KKT points as well as a corresponding GSIP-index are introduced in this paper. In particular, a nondegenerate KKT-point is a local minimizer if and only if its GSIP-index vanishes. (ProQuest: ... denotes formulae/symbols omitted.)