Further investigation on feasibility of mathematical programs with equilibrium constraints

In this paper, we present feasibility conditions for mathematical programs with affine equilibrium constraints (MPECs) where additional joint constraints are present that must be satisfied by the state and design variables of the problems. We show that these conditions are also sufficient for quadratic programming subproblems arising from the penalty interior point algorithm (PIPA) and the smooth sequential quadratic programming (SQP) algorithm for solving MPECs to be consistent.