Some Feasibility Issues in Mathematical Programs with Equilibrium Constraints

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Abstract
This paper is concerned with some feasibility issues in mathematical programs with equilibrium constraints (MPECs) where additional joint constraints are present that must be satisfied by the state and design variables of the problems. We introduce sufficient conditions that guarantee the feasibility of these MPECs. It turns out that these conditions also guarantee the feasibility of the quadratic programming (QP) subproblems arising from the penalty interior point algorithm (PIPA) and the sequential quadratic programming (SQP) algorithm for solving MPECs; thus the same conditions ensure that these algorithms are applicable for solving this class of jointly constrained MPECs.