A Fritz John approach to first order optimality conditions for mathematical programs with equilibrium constraints

Abstract. Mathematical programs with equilibrium constraints (MPECs) are nonlinear programs which do not satisfy any of the common constraint qualifications. In order to obtain first order optimality conditions, constraint qualifications tailored to MPECs have been developed and researched in the past. This has been done by falling back on technical proofs or results from nonsmooth analysis. In this paper, we use a completely dirfferent approach and show how the standard Fritz John conditions may be used in order to obtain the most important optimality conditions for MPECs. In this way, we obtain relatively short and elementary proofs for some known results in the MPEC field