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Fuzzy and exact optimality conditions for a bilevel set-valued problem via extremal principles. (English) Zbl 1251.90385
The paper considers a bilevel optimization problem where both the upper level and the lower level problem are set-valued optimization problems. Optimality conditions for weak local Pareto optimal solutions are proven based on two versions of the extremal principle inroduced by Mordukhovich 2001 and 2006. More precisely, approximate (fuzzy) necessary optimality conditions are derived based on the approximate extremal principle of Mordukhovich, while exact necessary optimality conditions are induced by the corresponding exact extremal principle.

MSC:
90C46 Optimality conditions and duality in mathematical programming
49K99 Optimality conditions
90C48 Programming in abstract spaces
90C29 Multi-objective and goal programming
90C70 Fuzzy and other nonstochastic uncertainty mathematical programming
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