an:07001119
Zbl 1427.90251
Lafhim, L.; Gadhi, N.; Hamdaoui, K.; Rahou, F.
Necessary optimality conditions for a bilevel multiobjective programming problem via a \(\Psi\)-reformulation
EN
Optimization 67, No. 12, 2179-2189 (2018).
00425818
2018
j
90C29
multiobjective optimization
Summary: In this paper, we are concerned with a bilevel multiobjective optimization problem \((P)\). First, using \(\Psi\), a function introduced by \textit{N. Gadhi} and \textit{S. Dempe} [J. Optim. Theory Appl. 155, No. 1, 100--114 (2012; Zbl 1267.90130)], we transform \((P)\) into a one level optimization problem \((P^\ast)\). Second, on terms of convexificators, using a scalarization technique, we derive a Karash-Kuhn-Tucker (KKT)-type necessary optimality conditions to the initial problem \((P)\) under a generalized Abadie constraint qualification without the assumption that the lower-level problem satisfies the Mangasarian Fromovitz constraint qualification. Some examples have been introduced to illustrate our results.
Zbl 1267.90130