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

In this paper, we introduce two new constraint qualifications for mathematical programs with equilibrium constraints. One of them is a relaxed version of the No Nonzero Abnormal Multiplier Constraint Qualification, and the other is an adaptation of the Constant Rank of Subspace Component. The new conditions have nice properties. Indeed, they have the local preservation property and imply the error bound property under mild assumptions. Thus, they can be used to extend some known results on stability and sensitivity analysis. Furthermore, they can also be used in the convergence analysis of several methods for solving mathematical programs with equilibrium constraints.