| Autor: |
DARDOUR, ZAKARYA, LAFHIM, LAHOUSSINE, KALMOUN, EL MOSTAFA |
| Předmět: |
|
| Zdroj: |
Journal of Applied & Numerical Optimization; 2024, Vol. 6 Issue 2, p153-175, 23p |
| Abstrakt: |
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 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. [ABSTRACT FROM AUTHOR] |
| Databáze: |
Complementary Index |
| Externí odkaz: |
|
