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Optimality conditions for set-valued optimization problems. (English) Zbl 0927.90095
Summary: The generalized contingent epiderivative of set-valued maps is introduced in this paper and its relationship to the contingent epiderivative is investigated. A unified necessary and sufficient optimality condition is derived in terms of the generalized contingent epiderivative. The existence of weak subgradients of set-valued maps is proved, and a sufficient optimality condition of set-valued optimization problems is obtained in terms of weak subgradients.

MSC:
90C29Multi-objective programming; goal programming
49J52Nonsmooth analysis (other weak concepts of optimality)