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Scalarizations and Lagrange multipliers for approximate solutions in the vector optimization problems with set-valued maps

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  • In this paper, we characterize approximate solutions of vector optimization problems with set-valued maps. We gives several characterizations of generalized subconvexlike set-valued functions(see [10]), which is a generalization of nearly subconvexlike functions introduced in [34]. We present alternative theorem and derived scalarization theorems for approximate solutions with generalized subconvexlike set-valued maps. And then, Lagrange multiplier theorems under generalized Slater constraint qualification are established.
    Mathematics Subject Classification: 90C29, 90C30, 90C46.

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