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Contractibility of the Solution Sets in Strictly Quasiconcave Vector Maximization on Noncompact Domains

Author

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  • N. Q. Huy

    (Hanoi Pedagogical University)

  • N. D. Yen

    (Vietnam Academy of Science and Technology)

Abstract

We study the contractibility of the efficient solution set of strictly quasiconcave vector maximization problems on (possibly) noncompact feasible domains. It is proved that the efficient solution set is contractible if at least one of the objective functions is strongly quasiconcave and any intersection of level sets of the objective functions is a compact (possibly empty) set. This theorem generalizes the main result of Benoist (Ref.1), which was established for problems on compact feasible domains.

Suggested Citation

  • N. Q. Huy & N. D. Yen, 2005. "Contractibility of the Solution Sets in Strictly Quasiconcave Vector Maximization on Noncompact Domains," Journal of Optimization Theory and Applications, Springer, vol. 124(3), pages 615-635, March.
    • Handle: RePEc:spr:joptap:v:124:y:2005:i:3:d:10.1007_s10957-004-1177-9
    DOI: 10.1007/s10957-004-1177-9
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    References listed on IDEAS

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    1. A. Daniilidis & N. Hadjisavvas & S. Schaible, 1997. "Connectedness of the Efficient Set for Three-Objective Quasiconcave Maximization Problems," Journal of Optimization Theory and Applications, Springer, vol. 93(3), pages 517-524, June.
    2. J. Benoist & N. Popovici, 2001. "Contractibility of the Efficient Frontier of Three-Dimensional Simply-Shaded Sets," Journal of Optimization Theory and Applications, Springer, vol. 111(1), pages 81-116, October.
    3. E. U. Choo & D. R. Atkins, 1983. "Connectedness in Multiple Linear Fractional Programming," Management Science, INFORMS, vol. 29(2), pages 250-255, February.
    4. J. Benoist, 2001. "Contractibility of the Efficient Set in Strictly Quasiconcave Vector Maximization," Journal of Optimization Theory and Applications, Springer, vol. 110(2), pages 325-336, August.
    5. J. Benoist, 1998. "Connectedness of the Efficient Set for Strictly Quasiconcave Sets," Journal of Optimization Theory and Applications, Springer, vol. 96(3), pages 627-654, March.
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