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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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