In this paper, we introduce a new generalized convexity notion for set-valued maps, called ic-cone-convexlikeness, and use it as the main tool to derive an alternative theorem and necessary conditions for efficient, weakly efficient, and Benson properly efficient solutions of the problem of minimizing a set-valued map subject to set-valued constraints. Our results are valid for a class of optimization problems broader than that of the problems considered in Refs. 1--6 and generalize the corresponding results of these references.
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Communicated by H. P. Benson
The author thanks the anonymous referees for their remarks.
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Sach, P.H. New Generalized Convexity Notion for Set-Valued Maps and Application to Vector Optimization. J Optim Theory Appl 125, 157–179 (2005). https://doi.org/10.1007/s10957-004-1716-4
- set-valued maps
- alternative theorems
- Benson proper efficiency