One-Parametric Semi-Infinite 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 $G( x,t,y ) \leq 0$ 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 $t_1 ,t_2 \in T$. 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.