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Stability and Scalarization for a Unified Vector Optimization Problem

Author

Listed:
  • Shiva Kapoor

    (University of Delhi)

  • C. S. Lalitha

    (University of Delhi South Campus)

Abstract

This paper aims at investigating the Painlevé–Kuratowski convergence of solution sets of a sequence of perturbed vector problems, obtained by perturbing the feasible set and the objective function of a unified vector optimization problem, in real normed linear spaces. We establish convergence results, both in the image and given spaces, under the assumptions of domination and strict domination properties. Moreover, scalarization techniques are employed to establish the Painlevé–Kuratowski convergence in terms of the solution sets of a sequence of scalarized problems.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:182:y:2019:i:3:d:10.1007_s10957-019-01514-x
    DOI: 10.1007/s10957-019-01514-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. 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.
    3. E. Miglierina & E. Molho, 2002. "Scalarization and Stability in Vector Optimization," Journal of Optimization Theory and Applications, Springer, vol. 114(3), pages 657-670, September.
    4. C. S. Lalitha & Prashanto Chatterjee, 2012. "Stability for Properly Quasiconvex Vector Optimization Problem," Journal of Optimization Theory and Applications, Springer, vol. 155(2), pages 492-506, November.
    5. C. S. Lalitha & Prashanto Chatterjee, 2012. "Stability and Scalarization of Weak Efficient, Efficient and Henig Proper Efficient Sets Using Generalized Quasiconvexities," Journal of Optimization Theory and Applications, Springer, vol. 155(3), pages 941-961, December.
    6. X. X. Huang, 2000. "Stability in vector-valued and set-valued optimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 52(2), pages 185-193, November.
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    Cited by:

    1. Shiva Kapoor & C. S. Lalitha, 2021. "Essential stability in unified vector optimization," Journal of Global Optimization, Springer, vol. 80(1), pages 161-175, May.

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