Zakarya Dardour, Lahoussine Lafhim, El Mostafa Kalmoun, Primal and dual second-order necessary optimality conditions in bilevel programming

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DOI: 10.23952/jano.6.2024.2.01
Volume 6, Issue 2, 1 August 2024, Pages 153-175

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 lower-level 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 $\Psi$ -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.

How to Cite this Article:
Z. Dardour, L. Lafhim, E.M. Kalmoun, Primal and dual second-order necessary optimality conditions in bilevel programming, J. Appl. Numer. Optim. 6 (2024), 153-175.