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Characterizations of the Set Less Order Relation in Nonconvex Set Optimization

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  • Johannes Jahn

    (Universität Erlangen-Nürnberg)

Abstract

For nonconvex set optimization problems based on the set less order relation, this paper presents characterizations of optimal sets and gives necessary conditions for set inequalities and non-optimal sets using directional derivatives. For specific order cones, the directional derivatives of known functionals describing the negative cones are also given.

Suggested Citation

  • Johannes Jahn, 2022. "Characterizations of the Set Less Order Relation in Nonconvex Set Optimization," Journal of Optimization Theory and Applications, Springer, vol. 193(1), pages 523-544, June.
    • Handle: RePEc:spr:joptap:v:193:y:2022:i:1:d:10.1007_s10957-021-01985-x
    DOI: 10.1007/s10957-021-01985-x
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    References listed on IDEAS

    as
    1. Johannes Jahn, 2015. "Vectorization in Set Optimization," Journal of Optimization Theory and Applications, Springer, vol. 167(3), pages 783-795, December.
    2. Magnus, Jan R., 1985. "On Differentiating Eigenvalues and Eigenvectors," Econometric Theory, Cambridge University Press, vol. 1(2), pages 179-191, August.
    3. Johannes Jahn, 2020. "Introduction to the Theory of Nonlinear Optimization," Springer Books, Springer, edition 4, number 978-3-030-42760-3, December.
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