In this paper, we deal with constraint qualifications, stationary concepts and
optimality conditions for a nonsmooth mathematical program with equilibrium
constraints (MPEC). The main tool in our study is the notion of convexificator.
Using this notion, standard and MPEC Abadie and several other constraint
qualifications are proposed and a comparison between them is presented. We
also define nonsmooth stationary conditions based on the convexificators. In
particular,we show that GS-stationary is the first-order optimality condition under
generalized standardAbadie constraint qualification. Finally, sufficient conditions
for global or local optimality are derived under someMPECgeneralized convexity
assumptions.
