Journal of Optimization Theory and Applications

, Volume 171, Issue 2, pp 402–421 | Cite as

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

  • Stephan DempeEmail author
  • Maria Pilecka


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.


Set optimisation Set relation Support function Directional derivative 

Mathematics Subject Classification

49J53 54C60 90C46 06A99 


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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Department of Mathematics and Computer ScienceTechnical University Bergakademie FreibergFreibergGermany

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