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Pointwise Well-Posedness of Perturbed Vector Optimization Problems in a Vector-Valued Variational Principle

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  • X. X. Huang

    (Chongqing Normal University)

Abstract

In this note, we point out and correct some errors in Ref. 1. Another type of pointwise well-posedness and strong pointwise well-posedness of vector optimization problems is introduced. Sufficient conditions to guarantee this type of well-posedness are provided for perturbed vector optimization problems in connection with the vector-valued Ekeland variational principle.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:108:y:2001:i:3:d:10.1023_a:1017595610700
    DOI: 10.1023/A:1017595610700
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    References listed on IDEAS

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    1. Guang Ya Chen & X. X. Huang, 1998. "Ekeland's ε-variational principle for set-valued mappings," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 48(2), pages 181-186, November.
    2. G. Y. Chen & X. X. Huang, 1998. "A unified approach to the existing three types of variational principles for vector valued functions," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 48(3), pages 349-357, December.
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    Citations

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    Cited by:

    1. Ya-ping Fang & Nan-jing Huang, 2007. "Increasing-along-rays property, vector optimization and well-posedness," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 65(1), pages 99-114, February.
    2. Onetti Alberto & Verma Sameer, 2008. "Licensing and Business Models," Economics and Quantitative Methods qf0806, Department of Economics, University of Insubria.
    3. 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.
    4. 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.
    5. Li Zhu & Fu-quan Xia, 2012. "Scalarization method for Levitin–Polyak well-posedness of vectorial optimization problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 76(3), pages 361-375, December.
    6. Rocca Matteo & Papalia Melania, 2008. "Well-posedness in vector optimization and scalarization results," Economics and Quantitative Methods qf0807, Department of Economics, University of Insubria.
    7. S. Li & W. Zhang, 2010. "Hadamard well-posed vector optimization problems," Journal of Global Optimization, Springer, vol. 46(3), pages 383-393, March.
    8. Elisa Mastrogiacomo & Matteo Rocca, 2021. "Set optimization of set-valued risk measures," Annals of Operations Research, Springer, vol. 296(1), pages 291-314, January.
    9. 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.
    10. 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.
    11. Jacqueline Morgan, 2005. "Approximations and Well-Posedness in Multicriteria Games," Annals of Operations Research, Springer, vol. 137(1), pages 257-268, July.
    12. M. Durea, 2007. "Scalarization for pointwise well-posed vectorial problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 66(3), pages 409-418, December.
    13. Giovanni P. Crespi & Mansi Dhingra & C. S. Lalitha, 2018. "Pointwise and global well-posedness in set optimization: a direct approach," Annals of Operations Research, Springer, vol. 269(1), pages 149-166, October.
    14. Miglierina Enrico & Molho Elena & Rocca Matteo, 2004. "Well-posedness and scalarization in vector optimization," Economics and Quantitative Methods qf0403, Department of Economics, University of Insubria.

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