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Essential stability in unified vector optimization

Author

Listed:
  • Shiva Kapoor

    (University of Delhi)

  • C. S. Lalitha

    (University of Delhi South Campus)

Abstract

The emphasis of the paper is to examine the essential stability of efficient solutions for semicontinuous vector optimization problems, subject to the perturbation of objective function and feasible set. We obtain sufficient conditions for existence and characterization of essential efficient solutions, essential sets and essential components, where the efficient solutions are governed by an arbitrary preference relation in a real normed linear space. Further, we establish the density of the set of stable vector optimization problems in the sense of Baire category. We also exhibit that essential stability is weaker than examining continuity aspects of solution sets.

Suggested Citation

  • Shiva Kapoor & C. S. Lalitha, 2021. "Essential stability in unified vector optimization," Journal of Global Optimization, Springer, vol. 80(1), pages 161-175, May.
    • Handle: RePEc:spr:jglopt:v:80:y:2021:i:1:d:10.1007_s10898-021-00996-2
    DOI: 10.1007/s10898-021-00996-2
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    References listed on IDEAS

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    4. Zai-Yun Peng & Jian-Wen Peng & Xian-Jun Long & Jen-Chih Yao, 2018. "On the stability of solutions for semi-infinite vector optimization problems," Journal of Global Optimization, Springer, vol. 70(1), pages 55-69, January.
    5. Q. Luo, 1999. "Essential Component and Essential Optimum Solution of Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 102(2), pages 433-438, August.
    6. Shiva Kapoor & C. S. Lalitha, 2019. "Stability and Scalarization for a Unified Vector Optimization Problem," Journal of Optimization Theory and Applications, Springer, vol. 182(3), pages 1050-1067, September.
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