JOHANNES KEPLER UNIVERSITY LINZ Institute of Computational Mathematics Second Order Conditions for Metric Subregularity of Smooth Constraint Systems

Metric subregularity (respectively calmness) of multifunctions is a property which is not stable under smooth perturbations, implying that metric subregularity cannot be fully characterized by first order theory. In this paper we derive second order conditions for metric subregularity, both sufficient and necessary, for multifunctions associated with constraint systems as they occur in optimization. We show that the main difference between the necessary and sufficient conditions is the replacement of an inequality by a strict inequality, just as in the case of ”no gap” second order optimality conditions in optimization.