MPCC: Strong Stability of M-stationary Points

Abstract

In this paper we study the class of mathematical programs with complementarity constraints MPCC. Under the Linear Independence constraint qualification MPCC-LICQ we state a topological as well as an equivalent algebraic characterization for the strong stability (in the sense of Kojima) of an M-stationary point for MPCC. By allowing perturbations of the describing functions up to second order, the concept of strong stability refers here to the local existence and uniqueness of an M-stationary point for any sufficiently small perturbed problem where this unique solution depends continuously on the perturbation. Finally, some relations to S- and C-stationarity are briefly discussed.

Strongly Stable Stationary Points for a Class of Generalized Equations

“…Thus, by Theorem 4.10, the mapping of Lagrange vectors \\theta (P ) is well defined and continuous in a neighborhood of \= P . However, this result has been already established in [18] for C-stationary points and in [8] for M-and S-stationary points.…”