ONE-PARAMETRIC SEMIINFINITE OPTIMIZATION - ON THE STABILITY OF THE FEASIBLE SET

This paper studies a global stability property of the (noncompact) feasible set M(H, G, t) of a semi-infinite optimization problem defined by finitely many equations H(x, t) = 0 and, perhaps, infinitely many inequalities G(x, t, y) less than or equal to 0 that depend on a real parameter t that varies in a compact parameter interval T. Global stability refers to the homeomorphy of M[H, G, t(1)] and M[H, G, t(2)] for any parameter values t(1), t(2) is an element of T. It is shown that the overall validity of a so-called extended Mangasarian-Fromovitz constraint qualification at infinity (a constraint qualification taking parameter information into account) is sufficient for the stability mentioned. Key words. one-parametric semi-infinite optimization, stability of the feasible set, homeomorphy, extended Mangasarian-Fromovitz constraint qualification at infinity