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Optimality conditions for the semivectorial bilevel optimization problem. (English) Zbl 1124.90028
Necessary optimality conditions for the optimistic bilevel programming problem with a parametric convex multiobjective programming problem in the lower level are derived. The optimality conditions use the contingent cone to the graph of the mapping of (weakly or properly) efficient solutions of the lower level problem which in general is difficult to compute. For the case of a parametric linear multiobjective lower-level problem the obtained conditions can be formulated as Karush-Kuhn-Tucker type conditions.

90C29 Multi-objective and goal programming
90C46 Optimality conditions and duality in mathematical programming
90C48 Programming in abstract spaces
91A65 Hierarchical games (including Stackelberg games)
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