Two New Weak Constraint Qualifications for Mathematical Programs with Equilibrium Constraints and Applications

We introduce two new weaker Constraint Qualifications (CQs) for mathematical programs with equilibrium (or complementarity) constraints, MPEC for short. One of them is a tailored version of the constant rank of subspace component (CRSC) and the other is a relaxed version of the MPECNo Nonzero Abnormal Multiplier Constraint Qualification (MPEC-NNAMCQ). Both incorporate the exact set of gradients of inequality constraints whose properties has to be preserved locally. MPECRNNAMCQ and MPEC-CRSC have nice properties: they have the local preservation property and imply the error bound property under mild assumption. Thus, they can be used to extend some results on perturbation analysis and sensitivity existing in the literature. Furthermore, both conditions can be also used in the global convergence analysis of several methods for solving MPECs. We discusse the relation between MPEC-RCPLD and MPEC-Abadie CQ.