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Some Remarks on Bi-level Vector Extremum Problems

In: Constructive Nonsmooth Analysis and Related Topics

Author

Listed:
  • Carla Antoni

    (Naval Academy)

  • Franco Giannessi

    (University of Pisa)

Abstract

The present note aims at introducing a new approach for handling bi-level vector extremum problems. After having defined a class of nonconvex functions on which it seems promising to carry on the research for such problems, the note is concentrated on the convex-linear bi-level problems; in this case, the results are compared with the existing literature. Suggestions for further research are given.

Suggested Citation

  • Carla Antoni & Franco Giannessi, 2014. "Some Remarks on Bi-level Vector Extremum Problems," Springer Optimization and Its Applications, in: Vladimir F. Demyanov & Panos M. Pardalos & Mikhail Batsyn (ed.), Constructive Nonsmooth Analysis and Related Topics, edition 127, pages 137-157, Springer.
    • Handle: RePEc:spr:spochp:978-1-4614-8615-2_9
    DOI: 10.1007/978-1-4614-8615-2_9
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    Citations

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    Cited by:

    1. Shengjie Li & Yangdong Xu & Manxue You & Shengkun Zhu, 2018. "Constrained Extremum Problems and Image Space Analysis–Part I: Optimality Conditions," Journal of Optimization Theory and Applications, Springer, vol. 177(3), pages 609-636, June.
    2. Carla Antoni & Mohammed Alshahrani, 2018. "Images, Fixed Points and Vector Extremum Problems," Journal of Optimization Theory and Applications, Springer, vol. 177(3), pages 889-905, June.
    3. Yangdong Xu & Pingping Zhang, 2018. "Connectedness of Solution Sets of Strong Vector Equilibrium Problems with an Application," Journal of Optimization Theory and Applications, Springer, vol. 178(1), pages 131-152, July.
    4. Erjiang Sun, 2017. "On Optimization Over the Efficient Set of a Multiple Objective Linear Programming Problem," Journal of Optimization Theory and Applications, Springer, vol. 172(1), pages 236-246, January.
    5. Carla Antoni & Franco Giannessi, 2018. "Images and Existence of Constrained Scalar and Vector Extrema," Journal of Optimization Theory and Applications, Springer, vol. 177(3), pages 865-888, June.
    6. Jiawei Chen & Shengjie Li & Zhongping Wan & Jen-Chih Yao, 2015. "Vector Variational-Like Inequalities with Constraints: Separation and Alternative," Journal of Optimization Theory and Applications, Springer, vol. 166(2), pages 460-479, August.

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