Second-Order Optimality Conditions for Mathematical Programs with Equilibrium Constraints
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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.
KeywordsMathematical program with equilibrium constraints Second-order optimality condition Constraint qualification Isolatedness
The first and second authors’ work was supported in part by NSFC Grant #11071028. The third author’s work was supported in part by NSERC. The authors are grateful to the two anonymous referees for their helpful comments and suggestions.
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