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A unified minimal solution in set optimization

Author

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  • Khushboo

    (University of Delhi)

  • C. S. Lalitha

    (University of Delhi South Campus)

Abstract

In this paper we extend the notion of minimal solutions for a vector optimization problem considered by Flores-Bazán et al. (J Optim Theory Appl 164:455–478, 2015) to a set-valued optimization problem, with both vector and set solution criteria. Also, we extend the Gerstewitz function proposed by Hernández and Rodríguez-Marín (J Math Anal Appl 325:1–18, 2007) and use it to scalarize minimal solutions with respect to set criterion. We also provide an existence result of minimal solutions with set criterion. Finally, we investigate links between the minimal solutions with respect to vector criterion and set criterion.

Suggested Citation

  • Khushboo & C. S. Lalitha, 2019. "A unified minimal solution in set optimization," Journal of Global Optimization, Springer, vol. 74(1), pages 195-211, May.
    • Handle: RePEc:spr:jglopt:v:74:y:2019:i:1:d:10.1007_s10898-019-00740-x
    DOI: 10.1007/s10898-019-00740-x
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    References listed on IDEAS

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    1. Fabián Flores-Bazán & Fernando Flores-Bazán & Sigifredo Laengle, 2015. "Characterizing Efficiency on Infinite-dimensional Commodity Spaces with Ordering Cones Having Possibly Empty Interior," Journal of Optimization Theory and Applications, Springer, vol. 164(2), pages 455-478, February.
    2. Yu Han & Nan-jing Huang, 2018. "Continuity and Convexity of a Nonlinear Scalarizing Function in Set Optimization Problems with Applications," Journal of Optimization Theory and Applications, Springer, vol. 177(3), pages 679-695, June.
    3. Pham Huu Sach & Le Anh Tuan, 2013. "New Scalarizing Approach to the Stability Analysis in Parametric Generalized Ky Fan Inequality Problems," Journal of Optimization Theory and Applications, Springer, vol. 157(2), pages 347-364, May.
    4. Khushboo & C. S. Lalitha, 2018. "Scalarizations for a unified vector optimization problem based on order representing and order preserving properties," Journal of Global Optimization, Springer, vol. 70(4), pages 903-916, April.
    5. S. Khoshkhabar-amiranloo & E. Khorram, 2015. "Pointwise well-posedness and scalarization in set optimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 82(2), pages 195-210, October.
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    Cited by:

    1. L. Q. Anh & T. Q. Duy & D. V. Hien, 2020. "Stability of efficient solutions to set optimization problems," Journal of Global Optimization, Springer, vol. 78(3), pages 563-580, November.
    2. Khushboo & C. S. Lalitha, 2023. "Characterizations of set order relations and nonlinear scalarizations via generalized oriented distance function in set optimization," Journal of Global Optimization, Springer, vol. 85(1), pages 235-249, January.
    3. Chuang-Liang Zhang & Nan-jing Huang, 2021. "Set Relations and Weak Minimal Solutions for Nonconvex Set Optimization Problems with Applications," Journal of Optimization Theory and Applications, Springer, vol. 190(3), pages 894-914, September.
    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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