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Necessary optimality conditions for a bilevel multiobjective programming problem via a $$\Psi$$-reformulation. (English) Zbl 1427.90251
Summary: In this paper, we are concerned with a bilevel multiobjective optimization problem $$(P)$$. First, using $$\Psi$$, a function introduced by N. Gadhi and 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.

##### MSC:
 90C29 Multi-objective and goal programming
##### Keywords:
multiobjective optimization
Full Text:
##### References:
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