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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