Primal and dual second-order necessary optimality conditions in bilevel programming
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Bibliographic record
Abstract
The purpose of this paper is to derive primal and dual second-order necessary optimality conditions for a standard bilevel optimization problem with both smooth and nonsmooth data.The approach involves utilizing two different reformulations of the hierarchical model as a single-level problem under a partial calmness assumption.The first reformulation consists on the use of the value function of the lowerlevel problem, which is then tackled by using second-order directional derivatives.However, for the dual conditions, this approach is not suitable except for cases that the value function is smooth.Therefore, we adopt a second approach that relies on the Ψ-reformulation.In both cases, the obtained necessary optimality conditions can be expressed according to the problem data.Finally, some examples are given to illustrate the proven results.
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