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Extended B-Well-Posedness and Property (H) for Set-Valued Vector Optimization with Convexity

Author

Listed:
  • Y. P. Fang

    (Sichuan University)

  • R. Hu

    (Chengdu University of Information Technology)

  • N. J. Huang

    (Sichuan University)

Abstract

The purpose of this paper is to study the extended well-posedness in the sense of Bednarczuk for set-valued vector optimization. This notion of well-posedness can be interpreted as some sort of well-posedness under perturbation in terms of Hausdorff set-convergence. To investigate the extended B-well-posedness, we generalize property (H) due to Miglierina and Molho to the set-valued and perturbed case. Under a convexity assumption, we show that the extended B-well-posedness is closely related to property (H).

Suggested Citation

  • Y. P. Fang & R. Hu & N. J. Huang, 2007. "Extended B-Well-Posedness and Property (H) for Set-Valued Vector Optimization with Convexity," Journal of Optimization Theory and Applications, Springer, vol. 135(3), pages 445-458, December.
    • Handle: RePEc:spr:joptap:v:135:y:2007:i:3:d:10.1007_s10957-007-9272-3
    DOI: 10.1007/s10957-007-9272-3
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    References listed on IDEAS

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    1. Bednarczuk, Ewa M., 2004. "Continuity of minimal points with applications to parametric multiple objective optimization," European Journal of Operational Research, Elsevier, vol. 157(1), pages 59-67, August.
    2. X. X. Huang, 2000. "Extended Well-Posedness Properties of Vector Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 106(1), pages 165-182, July.
    3. X. X. Huang, 2001. "Extended and strongly extended well-posedness of set-valued optimization problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 53(1), pages 101-116, April.
    4. T. Zolezzi, 2001. "Well-Posedness and Optimization under Perturbations," Annals of Operations Research, Springer, vol. 101(1), pages 351-361, January.
    5. M. Bianchi & N. Hadjisavvas & S. Schaible, 1997. "Vector Equilibrium Problems with Generalized Monotone Bifunctions," Journal of Optimization Theory and Applications, Springer, vol. 92(3), pages 527-542, March.
    6. E. Miglierina & E. Molho & M. Rocca, 2005. "Well-Posedness and Scalarization in Vector Optimization," Journal of Optimization Theory and Applications, Springer, vol. 126(2), pages 391-409, August.
    7. X. X. Huang, 2001. "Pointwise Well-Posedness of Perturbed Vector Optimization Problems in a Vector-Valued Variational Principle," Journal of Optimization Theory and Applications, Springer, vol. 108(3), pages 671-684, March.
    8. E. Miglierina & E. Molho, 2003. "Well-posedness and convexity in vector optimization," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 58(3), pages 375-385, December.
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    Cited by:

    1. 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.
    2. X. J. Long & J. W. Peng, 2013. "Generalized B-Well-Posedness for Set Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 157(3), pages 612-623, June.
    3. 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.
    4. Meenakshi Gupta & Manjari Srivastava, 2019. "Well-posedness and scalarization in set optimization involving ordering cones with possibly empty interior," Journal of Global Optimization, Springer, vol. 73(2), pages 447-463, February.

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