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Well-posedness and scalarization in set optimization involving ordering cones with possibly empty interior

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  • Meenakshi Gupta

    (University of Delhi)

  • Manjari Srivastava

    (University of Delhi)

Abstract

In this paper, we introduce three types of well-posedness for a set optimization problem (u-SOP). Some necessary and sufficient conditions for these well-posedness have been established. Two different scalar optimization problems involving a generalized oriented distance function have been considered. Characterization of u-minimal solutions of (u-SOP) in terms of solutions of these scalar optimization problems have been obtained. Finally, equivalence of well-posedness of (u-SOP) with well-posedness of these scalar optimization problems have been established.

Suggested Citation

  • Meenakshi Gupta & Manjari Srivastava, 2019. "Well-posedness and scalarization in set optimization involving ordering cones with possibly empty interior," Journal of Global Optimization, Springer, vol. 73(2), pages 447-463, February.
    • Handle: RePEc:spr:jglopt:v:73:y:2019:i:2:d:10.1007_s10898-018-0695-1
    DOI: 10.1007/s10898-018-0695-1
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    References listed on IDEAS

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    7. Y. P. Fang & R. Hu & N. J. Huang, 2007. "Extended B-Well-Posedness and Property (H) for Set-Valued Vector Optimization with Convexity," Journal of Optimization Theory and Applications, Springer, vol. 135(3), pages 445-458, December.
    8. C. Lalitha & Prashanto Chatterjee, 2014. "Levitin–Polyak well-posedness for constrained quasiconvex vector optimization problems," Journal of Global Optimization, Springer, vol. 59(1), pages 191-205, May.
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    Cited by:

    1. Meenakshi Gupta & Manjari Srivastava, 2020. "Approximate Solutions and Levitin–Polyak Well-Posedness for Set Optimization Using Weak Efficiency," Journal of Optimization Theory and Applications, Springer, vol. 186(1), pages 191-208, July.
    2. Kuntal Som & Vellaichamy Vetrivel, 2022. "A Note on Pointwise Well-Posedness of Set-Valued Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 192(2), pages 628-647, February.
    3. Kuntal Som & V. Vetrivel, 2023. "Global well-posedness of set-valued optimization with application to uncertain problems," Journal of Global Optimization, Springer, vol. 85(2), pages 511-539, February.
    4. Qamrul Hasan Ansari & Pradeep Kumar Sharma, 2022. "Some Properties of Generalized Oriented Distance Function and their Applications to Set Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 193(1), pages 247-279, June.

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