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Extended Well-Posedness Properties of Vector Optimization Problems

Author

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  • X. X. Huang

    (Chongqing Normal University)

Abstract

In this paper, the concept of extended well-posedness of scalar optimization problems introduced by Zolezzi is generalized to vector optimization problems in three ways: weakly extended well-posedness, extended well-posedness, and strongly extended well-posedness. Criteria and characterizations of the three types of extended well-posedness are established, generalizing most of the results obtained by Zolezzi for scalar optimization problems. Finally, a stronger vector variational principle and Palais-Smale type conditions are used to derive sufficient conditions for the three types of extended well-posedness.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:106:y:2000:i:1:d:10.1023_a:1004615325743
    DOI: 10.1023/A:1004615325743
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    References listed on IDEAS

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    1. 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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    Cited by:

    1. Onetti Alberto & Verma Sameer, 2008. "Licensing and Business Models," Economics and Quantitative Methods qf0806, Department of Economics, University of Insubria.
    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. Rocca Matteo & Papalia Melania, 2008. "Well-posedness in vector optimization and scalarization results," Economics and Quantitative Methods qf0807, Department of Economics, University of Insubria.
    4. S. Li & W. Zhang, 2010. "Hadamard well-posed vector optimization problems," Journal of Global Optimization, Springer, vol. 46(3), pages 383-393, March.
    5. G. P. Crespi & M. Papalia & M. Rocca, 2009. "Extended Well-Posedness of Quasiconvex Vector Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 141(2), pages 285-297, May.
    6. 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.
    7. Jacqueline Morgan, 2005. "Approximations and Well-Posedness in Multicriteria Games," Annals of Operations Research, Springer, vol. 137(1), pages 257-268, July.
    8. 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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