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Stability in vector-valued and set-valued optimization

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  • X. X. Huang

Abstract

In this paper, we discuss the stability of the sets of efficient points of vector-valued and set-valued optimization problems when the data (E n ,f n ) (resp. (E n , F n )) of the approximate problems converge to the data (E, f) (resp. (E, F)) of the original problem in the sense of Painleve-Kuratowski or Mosco. Our results improve and generalize those obtained by Attouch and Riahi in Section 5 in [1]. Copyright Springer-Verlag Berlin Heidelberg 2000

Suggested Citation

  • 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.
    • Handle: RePEc:spr:mathme:v:52:y:2000:i:2:p:185-193
    DOI: 10.1007/s001860000085
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    Cited by:

    1. S. W. Xiang & W. S. Yin, 2007. "Stability Results for Efficient Solutions of Vector Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 134(3), pages 385-398, September.
    2. Xiao-Bing Li & Qi-Lin Wang & Zhi Lin, 2016. "Stability of Set-Valued Optimization Problems with Naturally Quasi-Functions," Journal of Optimization Theory and Applications, Springer, vol. 168(3), pages 850-863, March.
    3. Shiva Kapoor & C. S. Lalitha, 2019. "Stability in unified semi-infinite vector optimization," Journal of Global Optimization, Springer, vol. 74(2), pages 383-399, June.
    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. 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.
    6. 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.
    7. Rubén López, 2013. "Variational convergence for vector-valued functions and its applications to convex multiobjective optimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 78(1), pages 1-34, August.

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