Mathematical Programs with Complementarity Constraints: Stationarity, Optimality, and Sensitivity

We study mathematical programs with complementarity constraints. Several stationarity concepts, based on a piecewise smooth formulation, are presented and compared. The concepts are related to stationarity conditions for certain smooth programs as well as to stationarity concepts for a nonsmooth exact penalty function. Further, we present Fiacco-McCormick type second order optimality conditions and an extension of the stability results of Robinson and Kojima to mathematical programs with complementarity constraints.