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On the solution continuity of parametric set optimization problems

Author

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  • Y. D. Xu

    (Chongqing University of Posts and Telecommunications)

  • S. J. Li

    (Chongqing University)

Abstract

The aim of this paper is to investigate the continuity of the solution set maps of set-valued vector optimization problems with set optimization criterion. First, we introduce a new concept, which is called a u-lower level map. Then, we give some sufficient conditions for the upper and lower semicontinuities of the generalized lower level map. Finally, by virtue of the semicontinuity of the u-lower level map, we obtain the continuity of the minimal solution set map to parametric set-valued vector optimization problems with set optimization criterion.

Suggested Citation

  • Y. D. Xu & S. J. Li, 2016. "On the solution continuity of parametric set optimization problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 84(1), pages 223-237, August.
    • Handle: RePEc:spr:mathme:v:84:y:2016:i:1:d:10.1007_s00186-016-0541-5
    DOI: 10.1007/s00186-016-0541-5
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    References listed on IDEAS

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    1. Joël Benoist & Nicolae Popovici, 2003. "Characterizations of convex and quasiconvex set-valued maps," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 57(3), pages 427-435, August.
    2. Xian-Jun Long & Jian-Wen Peng & Zai-Yun Peng, 2015. "Scalarization and pointwise well-posedness for set optimization problems," Journal of Global Optimization, Springer, vol. 62(4), pages 763-773, August.
    3. 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.
    4. 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.
    5. 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.
    6. Johannes Jahn, 2015. "A derivative-free descent method in set optimization," Computational Optimization and Applications, Springer, vol. 60(2), pages 393-411, March.
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    Cited by:

    1. Lam Quoc Anh & Tran Quoc Duy & Dinh Vinh Hien & Daishi Kuroiwa & Narin Petrot, 2020. "Convergence of Solutions to Set Optimization Problems with the Set Less Order Relation," Journal of Optimization Theory and Applications, Springer, vol. 185(2), pages 416-432, May.
    2. Pham Huu Sach, 2018. "Stability Property in Bifunction-Set Optimization," Journal of Optimization Theory and Applications, Springer, vol. 177(2), pages 376-398, May.

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