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$E$-super efficiency of set-valued optimization problems involving improvement sets

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  • In this paper, $E$-super efficiency of set-valued optimization problems is investigated. Firstly, based on the improvement set, a new notion of $E$-super efficient point is introduced in real locally convex spaces. Secondly, under the assumption of near $E$-subconvexlikeness of set-valued maps, scalarization theorems of set-valued optimization problems are established in the sense of $E$-super efficiency. Finally, Lagrange multiplier theorems of set-valued optimization problems are obtained in the sense of $E$-super efficiency.
    Mathematics Subject Classification: 90C26, 90C29, 90C30.

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