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Polar Conic Set-Valued Map in Vector Optimization. Continuity and Derivability

Author

Listed:
  • P. Jiménez Guerra

    (U.N.E.D.)

  • M. A. Melguizo

    (Universidad de Alicante)

  • M. J. Muñoz-Bouzo

    (U.N.E.D.)

Abstract

In the context of vector optimization, several results are stated mainly about the continuity and the derivability of a conic set-valued map (the polar conic function) having a close relation with the positive efficient points, the ideal points and other distinguished elements of the efficient line. The contingent cone to the set of the general positive quasiefficient points at a point x 0 is also related with the frontier of the dual cone of the image at x 0 of the polar conic function.

Suggested Citation

  • P. Jiménez Guerra & M. A. Melguizo & M. J. Muñoz-Bouzo, 2009. "Polar Conic Set-Valued Map in Vector Optimization. Continuity and Derivability," Journal of Optimization Theory and Applications, Springer, vol. 142(2), pages 343-354, August.
    • Handle: RePEc:spr:joptap:v:142:y:2009:i:2:d:10.1007_s10957-009-9542-3
    DOI: 10.1007/s10957-009-9542-3
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    References listed on IDEAS

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    1. Ballve, M. E. & Jimenez Guerra, P., 2005. "Some geometrical aspects of the efficient line in vector optimization," European Journal of Operational Research, Elsevier, vol. 162(2), pages 497-502, April.
    2. Balbas, A. & Ballve, M. & Jimenez Guerra, P., 2001. "Density theorems for ideal points in vector optimization," European Journal of Operational Research, Elsevier, vol. 133(2), pages 260-266, January.
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