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Second order optimality conditions for bilevel set optimization problems. (English) Zbl 1190.90179
Summary: In this work, we use the notion of the support function to the feasible set mapping to establish second order necessary and sufficient optimality conditions for the optimistic case of bilevel optimization problems. The main tools we exploit are approximate Jacobians, approximate Hessians, second order approximations and second order contingent sets.

MSC:
90C29 Multi-objective and goal programming
49J52 Nonsmooth analysis
90C30 Nonlinear programming
49K99 Optimality conditions
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