Abstract
This paper investigates set optimization problems in finite dimensional spaces with the property that the images of the set-valued objective map are described by inequalities and equalities and that sets are compared with the set less order relation. For these problems new Karush–Kuhn–Tucker conditions are shown as necessary and sufficient optimality conditions. Optimality conditions without multiplier of the objective map are also presented. The usefulness of these results is demonstrated with a standard example.
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Acknowledgements
The author thanks Diethard Klatte (University of Zürich) for his advice concerning Lemma 2.2 and anonymous referees for valuable suggestions, which essentially improved this paper.
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Communicated by Lionel Thibault.
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Jahn, J. Karush–Kuhn–Tucker Conditions in Set Optimization. J Optim Theory Appl 172, 707–725 (2017). https://doi.org/10.1007/s10957-017-1066-7
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DOI: https://doi.org/10.1007/s10957-017-1066-7