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Sufficient optimality conditions and duality results for a bilevel multiobjective optimization problem via a $$\Psi$$ reformulation. (English) Zbl 1433.90151
Summary: In this paper, we are concerned with a bilevel multiobjective optimization problem $$(P)$$. Using the function $$\Psi$$ introduced by the first author and S. Dempe [J. Optim. Theory Appl. 155, No. 1, 100–114 (2012; Zbl 1267.90130)], we reformulate $$(P)$$ as a single level mathematical programming problem $$(P^*)$$ and establish/exhibit the global equivalence between the two problems $$(P)$$ and $$(P^*)$$. Using a generalized convexity introduced by J. Dutta and S. Chandra [Optimization 53, No. 1, 77–94 (2004; Zbl 1079.90104)], we derive sufficient optimality conditions for the problem $$(P)$$ and establish Mond-Weir duality results. To illustrate the obtained results some examples are given.
##### MSC:
 90C29 Multi-objective and goal programming 90C46 Optimality conditions and duality in mathematical programming 49J52 Nonsmooth analysis
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