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Contractibility of the Efficient Frontier of Three-Dimensional Simply-Shaded Sets

Author

Listed:
  • J. Benoist

    (University of Limoges)

  • N. Popovici

    (Babes-Bolyai University)

Abstract

The aim of this paper is to study the geometrical and topological structure of the efficient frontier of simply-shaded sets in a three-dimensional Euclidean space with respect to the usual positive cone. Our main result concerns the contractibility of the efficient frontier and refines a recent result of Daniilidis, Hadjisavvas, and Schaible (Ref. 1) regarding the connectedness of the efficient outcome set for three-criteria optimization problems involving continuous semistrictly quasiconcave objective functions.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:111:y:2001:i:1:d:10.1023_a:1017571214523
    DOI: 10.1023/A:1017571214523
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    References listed on IDEAS

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    1. Bonnisseau, Jean-Marc & Cornet, Bernard, 1988. "Existence of equilibria when firms follow bounded losses pricing rules," Journal of Mathematical Economics, Elsevier, vol. 17(2-3), pages 119-147, April.
    2. 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.
    3. 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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    1. A. Daniilidis & Y. Garcia Ramos, 2007. "Some Remarks on the Class of Continuous (Semi-) Strictly Quasiconvex Functions," Journal of Optimization Theory and Applications, Springer, vol. 133(1), pages 37-48, April.
    2. 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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