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Lagrangian duality in set-valued optimization. (English) Zbl 1129.49029
Summary: We study optimization problems where the objective function and the binding constraints are set-valued maps and the solutions are defined by means of set-relations among all the images sets [{\it D. Kuroiwa}, in: Takahashi, W., Tanaka, T. (eds.) Nonlinear analysis and convex analysis, Proc. 1st international conference (NACA98), Niigata, Japan, Singapore: World Scientific, 221--228 (1999; Zbl 1003.49026)]. We introduce a new dual problem, establish some duality theorems and obtain a Lagrangian multiplier rule of nonlinear type under convexity assumptions. A necessary condition and a sufficient condition for the existence of saddle points are given.

MSC:
49J53Set-valued and variational analysis
49N15Duality theory (optimization)
90C46Optimality conditions, duality
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References:
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