Second‐Order Optimality Conditions for Mathematical Programs with Equilibrium Constraints

We study second‐order optimality conditions for mathematical programs with equilibrium constraints (MPEC). Firstly, we improve some second‐order optimality conditions for standard nonlinear programming problems using some newly discovered constraint qualifications in the literature, and apply them to MPEC. Then, we introduce some MPEC variants of these new constraint qualifications, which are all weaker than the MPEC linear independence constraint qualification, and derive several second‐order optimality conditions for MPEC under the new MPEC constraint qualifications. Finally, we discuss the isolatedness of local minimizers for MPEC under very weak conditions.