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Connectedness of the Efficient Set for Three-Objective Quasiconcave Maximization Problems

Author

Listed:
  • A. Daniilidis

    (University of the Aegean)

  • N. Hadjisavvas

    (University of the Aegean)

  • S. Schaible

    (University of California)

Abstract

For three-objective maximization problems involving continuous, semistrictly quasiconcave functions over a compact convex set, it is shown that the set of efficient solutions is connected. With that, an open problem stated by Choo, Schaible, and Chew in 1985 is solved.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:93:y:1997:i:3:d:10.1023_a:1022634827916
    DOI: 10.1023/A:1022634827916
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    Citations

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    Cited by:

    1. E. K. Makarov & N. N. Rachkovski, 2001. "Efficient Sets of Convex Compacta are Arcwise Connected," Journal of Optimization Theory and Applications, Springer, vol. 110(1), pages 159-172, July.
    2. 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.
    3. Riccardo Cambini & Laura Carosi & Laura Martein, 2017. "Generating the efficient frontier of a class of bicriteria generalized fractional programming," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 40(1), pages 81-101, November.
    4. 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.
    5. S.T. Hackman & U. Passy, 2002. "Maximizing a Linear Fractional Function on a Pareto Efficient Frontier," Journal of Optimization Theory and Applications, Springer, vol. 113(1), pages 83-103, April.
    6. A. Daniilidis & N. Hadjisavvas, 1999. "Characterization of Nonsmooth Semistrictly Quasiconvex and Strictly Quasiconvex Functions," Journal of Optimization Theory and Applications, Springer, vol. 102(3), pages 525-536, September.
    7. 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.
    8. 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.
    9. D. T. Luc & S. Schaible, 1997. "Efficiency and Generalized Concavity," Journal of Optimization Theory and Applications, Springer, vol. 94(1), pages 147-153, July.
    10. 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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