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Efficient Sets of Convex Compacta are Arcwise Connected

Author

Listed:
  • E. K. Makarov

    (National Academy of Sciences of Belarus)

  • N. N. Rachkovski

    (Belorussian State Pedagogical University)

Abstract

We prove that the efficient point set Max(Q|K) of a compact convex set Q⊂X in a Hausdorff topological vector space X ordered by a closed convex pointed cone K⊂X with nonempty K +i:={l⊂K\{0}:l(x)>0} is arcwise connected.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:110:y:2001:i:1:d:10.1023_a:1017599614183
    DOI: 10.1023/A:1017599614183
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    References listed on IDEAS

    as
    1. X. Y. Zheng, 2000. "Contractibility and Connectedness of Efficient Point Sets," Journal of Optimization Theory and Applications, Springer, vol. 104(3), pages 717-737, March.
    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.
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