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Necessary optimality conditions of a D.C. set-valued bilevel optimization problem. (English) Zbl 1152.90587
Summary: We consider a bilevel vector optimization problem where objective and constraints are set valued maps. Our approach consists of using a support function together with the convex separation principle for the study of necessary optimality conditions for D.C. bilevel set-valued optimization problems. We give optimality conditions in terms of the strong subdifferential of a cone-convex set-valued mapping introduced by J. Baier and J. Jahn [J. Optim. Theory Appl. 100, No. 1, 233–240 (1999; Zbl 0922.90118)], and the weak subdifferential of a cone-convex set-valued mapping of T. Tanino and Y. Sawaragi [J. Optimization Theory Appl. 31, 473–499 (1980; Zbl 0418.90080)] . The bilevel set-valued problem is transformed into a one level set-valued optimization problem using a transformation originated by J.J. Ye and D.L. Zhu [Optimization 33, No. 1, 9–27 (1995; Zbl 0820.65032)]. An example illustrating the usefulness of our result is also given.

MSC:
90C29 Multi-objective and goal programming
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