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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

Citations:

Zbl 1267.90130
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References:

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