Kybernetika 46 no. 3, 423-434, 2010

A Note on the Relation Between Strong and M-Stationarity for a Class of Mathematical Programs with Equilibrium Constraints

René Henrion, Jiří Outrata and Thomas Surowiec


\noindent In this paper, we deal with strong stationarity conditions for mathematical programs with equilibrium constraints (MPEC). The main task in deriving these conditions consists in calculating the Fréchet normal cone to the graph of the solution mapping associated with the underlying generalized equation of the MPEC. We derive an inner approximation to this cone, which is exact under an additional assumption. Even if the latter fails to hold, the inner approximation can be used to check strong stationarity via the weaker (but easier to calculate) concept of M-stationarity.


mathematical programs with equilibrium constraints, S-stationary points, M-stationary points, Fréchet normal cone, limiting normal cone


90C30, 49J53