Semi-infinite optimization : structure and stability of the feasible set

The problem of the minimization of a function f:R super(n) arrow right R under finitely many equality constraints and perhaps infinitely many inequality constraints gives rise to a structural analysis of the feasible set M(H, G) = (x epsilon R super(n)!H (x) = 0, G(x, y) greater than or equal to 0, y epsilon Y) with compact Y included in R super(r). An extension of the well-known Mangasarian-Fromovitz constraint qualification (EMFCQ) is introduced. The main result for compact M(H, G) is the equivalence of the topological stability of the feasible set M(H, G) and the validity of EMFCQ.