Parametric global optimization: sensitivity

Hubertus Th. Jongen, Jan-J. Rückmann and Oliver Stein

Abstract. For finite dimensional optimization problems with infinitely many inequality constraints ("semi-infinite" optimization), the topological concept of global stability and its algebraic characterization are introduced. Global stability refers to perturbations of the defining functions and their derivatives up to second order. Then, transitions between stable problems via one-parametric families are considered. Necessarily, certain unstable situations will be met and they will be discussed by means of the underlying singularities