In this paper we study constraint qualifications and optimality conditions for bilevel programming problems. We strive to derive checkable constraint qualifications in terms of problem data and applicable optimality conditions. For the bilevel program with convex lower level program we discuss drawbacks of reformulating a bilevel programming problem by the mathematical program with complementarity constraints and present a new sharp necessary optimality condition for the reformulation by the mathematical program with a generalized equation constraint. For the bilevel program with a nonconvex lower level program we propose a relaxed constant positive linear dependence (RCPLD) condition for the combined program.
Second-Order Necessary Conditions, Constraint Qualifications and Exact Penalty for Mathematical Programs with Switching Constraints
Bilevel Optimization under Uncertainty
Tight error bounds for log-determinant cones without constraint qualifications
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