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

Author

Listed:
  • Stephan Dempe

    (Technical University Bergakademie Freiberg)

  • Maria Pilecka

    (Technical University Bergakademie Freiberg)

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.

Suggested Citation

  • Stephan Dempe & Maria Pilecka, 2016. "Optimality Conditions for Set-Valued Optimisation Problems Using a Modified Demyanov Difference," Journal of Optimization Theory and Applications, Springer, vol. 171(2), pages 402-421, November.
    • Handle: RePEc:spr:joptap:v:171:y:2016:i:2:d:10.1007_s10957-015-0745-5
    DOI: 10.1007/s10957-015-0745-5
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    References listed on IDEAS

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    1. Y. Gao, 2000. "Demyanov Difference of Two Sets and Optimality Conditions of Lagrange Multiplier Type for Constrained Quasidifferentiable Optimization," Journal of Optimization Theory and Applications, Springer, vol. 104(2), pages 377-394, February.
    2. Jonas Ide & Elisabeth Köbis, 2014. "Concepts of efficiency for uncertain multi-objective optimization problems based on set order relations," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 80(1), pages 99-127, August.
    3. Y. Gao, 2006. "Differences of Polyhedra in Matrix Space and Their Applications to Nonsmooth Analysis," Journal of Optimization Theory and Applications, Springer, vol. 130(3), pages 431-442, September.
    Full references (including those not matched with items on IDEAS)

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