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Contractibility and Connectedness of Efficient Point Sets

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  • X. Y. Zheng

    (Yunnan University)

Abstract

Using the technique of space theory and set-valued analysis, we establish contractibility results for efficient point sets in a locally convex space and a path connectedness result for a positive proper efficient point set in a reflexive space. We also prove a connectedness result for a positive proper efficient point set in a locally convex space; as an application, we give a connectedness result for an efficient solution set in a locally convex space.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:104:y:2000:i:3:d:10.1023_a:1004649928081
    DOI: 10.1023/A:1004649928081
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    References listed on IDEAS

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    1. X. Y. Zheng, 1998. "Generalizations of a Theorem of Arrow, Barankin, and Blackwell in Topological Vector Spaces," Journal of Optimization Theory and Applications, Springer, vol. 96(1), pages 221-233, January.
    2. Schecter, Stephen, 1978. "Structure of the demand function and Pareto optimal set with natural boundary conditions," Journal of Mathematical Economics, Elsevier, vol. 5(1), pages 1-21, March.
    3. E. U. Choo & D. R. Atkins, 1983. "Connectedness in Multiple Linear Fractional Programming," Management Science, INFORMS, vol. 29(2), pages 250-255, February.
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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.

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