an:07239390
Zbl 07239390
Gadhi, Nazih Abderrazzak; El Idrissi, Mohammed; Hamdaoui, Khadija
Necessary optimality conditions for a semivectorial bilevel optimization problem using the kth-objective weighted-constraint approach
EN
Positivity 24, No. 4, 1111-1134 (2020).
00452385
2020
j
90C29 90C26 90C70 49K99
constraint qualification; limiting subdifferential; limiting normal cone; optimality condition; semivectorial bilevel program; weakly efficient solution
Summary: In this paper, we have pointed out that the proof of Theorem 11 in the recent paper [\textit{L. Lafhim}, Positivity 24, No. 2, 395--413 (2020; Zbl 07193703)] is erroneous. Using techniques from variational analysis, we propose other proofs to detect necessary optimality conditions in terms of Karush-Kuhn-Tucker multipliers. Our main results are given in terms of the limiting subdifferentials and the limiting normal cones. Completely detailed first order necessary optimality conditions are then given in the smooth setting while using the generalized differentiation calculus of Mordukhovich.
Zbl 07193703