Necessary and Sufficient Optimality Conditions for Optimization Problems with Complementarity Constraints

Jane Ye

ABSTRACT. Optimization problems with complementarity constraints are a class of nonlinear programming problems where all or parts of the constraints are complementarity systems. These problems are in general nonconvex and do not satisfy the usual constraint qualifications. In this talk we give sharp necessary optimality conditions involving Mordukhovich and proximal coderivatives that may hold even when the usual KKT conditions do not hold. The necessary conditions involving the proximal coderivatives turn out to be sufficient when the problem is ``convex''. The optimality conditions involving the proximal coderivatives are shown to be equivalent to a system of linear and nonlinear equations. Applications to bilevel programming problems will be also discussed.


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