Optimality Conditions for Set-Valued Optimisation Problems Using a Modified Demyanov Difference

Stephan Dempe () and Maria Pilecka ()
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Stephan Dempe: Technical University Bergakademie Freiberg
Maria Pilecka: Technical University Bergakademie Freiberg

Journal of Optimization Theory and Applications, 2016, vol. 171, issue 2, No 5, 402-421

Abstract: Abstract The aim of this paper was to provide optimality conditions for set-valued optimisation problems with respect to the set less order relation. For this purpose, we use a slightly modified Demyanov difference in order to introduce a sort of directional derivative for set-valued maps, which allows us to derive optimality conditions. Some results on existence and boundedness of the directional derivative are also given.

Keywords: Set optimisation; Set relation; Support function; Directional derivative; 49J53; 54C60; 90C46; 06A99 (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s10957-015-0745-5

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