Characterization of strong stability for C-stationary points in MPCC

Abstract

We study mathematical programs with complementarity constraints (MPCC). Special focus will be on C-stationary points. Under the Linear Independence Constraint Qualification we characterize strong stability of C-stationary points (in the sense of Kojima) by means of first and second order information of the defining functions. It turns out that strong stability of C-stationary points allows a possible degeneracy of bi-active Lagrange multipliers. Some relations to other stationarity concepts (such as A-, M-, S- and B-stationarity) are shortly discussed.