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Sublinear scalarizations for proper and approximate proper efficient points in nonconvex vector optimization

Author

Listed:
  • Fernando García-Castaño

    (University of Alicante)

  • Miguel Ángel Melguizo-Padial

    (University of Alicante)

  • G. Parzanese

    (University of Alicante)

Abstract

We show that under a separation property, a $${{{\mathcal {Q}}}}$$ Q -minimal point in a normed space is the minimum of a given sublinear function. This fact provides sufficient conditions, via scalarization, for nine types of proper efficient points; establishing a characterization in the particular case of Benson proper efficient points. We also obtain necessary and sufficient conditions in terms of scalarization for approximate Benson and Henig proper efficient points. The separation property we handle is a variation of another known property and our scalarization results do not require convexity or boundedness assumptions.

Suggested Citation

  • Fernando García-Castaño & Miguel Ángel Melguizo-Padial & G. Parzanese, 2023. "Sublinear scalarizations for proper and approximate proper efficient points in nonconvex vector optimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 97(3), pages 367-382, June.
    • Handle: RePEc:spr:mathme:v:97:y:2023:i:3:d:10.1007_s00186-023-00818-z
    DOI: 10.1007/s00186-023-00818-z
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    References listed on IDEAS

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    1. X. Y. Zheng, 1997. "Proper Efficiency in Locally Convex Topological Vector Spaces," Journal of Optimization Theory and Applications, Springer, vol. 94(2), pages 469-486, August.
    2. X. Y. Zheng, 2000. "Scalarization of Henig Proper Efficient Points in a Normed Space," Journal of Optimization Theory and Applications, Springer, vol. 105(1), pages 233-247, April.
    3. E. K. Makarov & N. N. Rachkovski, 1999. "Unified Representation of Proper Efficiency by Means of Dilating Cones," Journal of Optimization Theory and Applications, Springer, vol. 101(1), pages 141-165, April.
    4. Matthias Ehrgott, 2005. "Multicriteria Optimization," Springer Books, Springer, edition 0, number 978-3-540-27659-3, December.
    5. Gabriele Eichfelder & Refail Kasimbeyli, 2014. "Properly optimal elements in vector optimization with variable ordering structures," Journal of Global Optimization, Springer, vol. 60(4), pages 689-712, December.
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