Constraint Qualifications for Mathematical Programs with Equilibrium Constraints and their Local Preservation Property

This paper studies the system of constraint qualifications tailored for mathematical programs with equilibrium constraints. The main focuses are on the relations among them and their local preservation property. After giving a relaxed version of the constant positive linear dependence constraint qualification for mathematical programs with equilibrium constraints, we establish some new relations among the tailored constraint qualifications. Then, we investigate their local preservation property. Finally, we present several results on the isolatedness of local minimizers. The paper contains some proof techniques that seem to be new in the literature of mathematical programs with equilibrium constraints. The obtained results complement and improve some recent ones in this direction.