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Contractibility of the Efficient Set in Strictly Quasiconcave Vector Maximization

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  • J. Benoist

Abstract

In this paper, we investigate the contractibility of the efficient frontier in a vector maximization problem defined by a continuous vector-valued strictly quasiconcave function $$g = (g_1 ,...,g_n )$$ and a convex compact set D in ℝ p . It is shown that the efficient frontier is contractible if one of the components of g is strongly quasiconcave on X. This work extends a result by Sun (see Ref. 1), which confirms the connectedness of the efficient frontier.

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  • 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.
    • Handle: RePEc:spr:joptap:v:110:y:2001:i:2:d:10.1023_a:1017527329601
    DOI: 10.1023/A:1017527329601
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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, 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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    Cited by:

    1. Davide LA TORRE & Nicolae POPOVICI & Matteo ROCCA, 2008. "Scalar characterization of explicitly quasiconvex set-valued maps," Departmental Working Papers 2008-01, Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano.
    2. N. T. T. Huong & J.-C. Yao & N. D. Yen, 2020. "Geoffrion’s proper efficiency in linear fractional vector optimization with unbounded constraint sets," Journal of Global Optimization, Springer, vol. 78(3), pages 545-562, November.
    3. 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.

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