Abstract
Nowadays set-valued optimization means set-valued analysis and its application to optimization, and it is an extension of continuous optimization to the set-valued case. In this research area, one investigates optimization problems with constraints and/or an objective function described by set-valued maps, or investigations in set-valued analysis are applied to standard optimization problems. In this article, we are concerned with a set-valued optimization problem (P). Using a notion of approximation derived from Jourani and Thibault, we give necessary and sufficient optimality conditions for (P). Based on necessary optimality conditions given by Amahroq and Gadhi [2] (see Theorem 8), our approach consists of formulating the Mond–Weir dual problem (D) and establishing duality theorems for (P) and (D) without any constraint qualification.
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