Exact penalization of mathematical programs with equilibrium constraints

We study theoretical and computational aspects of an exact penalization app roach to mathematical programs with equilibrium constraints (MPECs). In the first part, we prove that a Mangasarian-Fromovitz-type condition ensures t he existence of a stable local error bound at the root of a real-valued non negative piecewise smooth function. A specification to nonsmooth formulatio ns of equilibrium constraints, e.g., complementarity conditions or normal e quations, provides conditions which guarantee the existence of a nonsmooth exact penalty function for MPECs. In the second part, we study a trust regi on minimization method for a class of composite nonsmooth functions which c omprises exact penalty functions arising from MPECs. We prove a global conv ergence result for the general method and incorporate a penalty update rule . A further specification results in an SQP trust region method for MPECs b ased on an l(1) penalty function.