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Stability of Set-Valued Optimization Problems with Naturally Quasi-Functions

Author

Listed:
  • Xiao-Bing Li

    (Chongqing Jiaotong University)

  • Qi-Lin Wang

    (Chongqing Jiaotong University)

  • Zhi Lin

    (Chongqing Jiaotong University)

Abstract

In this paper, we discuss the stability of three kinds of minimal point sets and three kinds of minimizer sets of naturally quasi-functional set-valued optimization problems when the data of the approximate problems converges to the data of the original problems in the sense of Painlevé–Kuratowski. Our main results improve and extend the results of the recent papers.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:168:y:2016:i:3:d:10.1007_s10957-015-0802-0
    DOI: 10.1007/s10957-015-0802-0
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    References listed on IDEAS

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    1. G. Y. Chen & X. X. Huang, 1998. "Stability results for Ekeland's ε variational principle for vector valued functions," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 48(1), pages 97-103, September.
    2. 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.
    3. 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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