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Characterizations of efficient solutions under polyhedrality assumptions

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Summary

We give several characterizations of efficient solutions of subsets ofR p (with respect to compatible preorders) in terms of the lexicographical order, under the assumptions that the set of admissible points is a convex polyhedron or the nonnegative cone corresponding to the preorder is polyhedral. We also characterize the lexicographical minimum of a convex polyhedron by means of the componentwise order and unitary lower triangular matrices.

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References

  • Benson HP (1979) An improved definition of proper efficiency for vector minimization with respect to cones. J Math Anal Appl 71:232–241

    Google Scholar 

  • Borwein JM (1980) Lexicographic multipliers. J Math Anal Appl 78:309–327

    Google Scholar 

  • Gorokhovik V (1986) Dual characteristics of minimality in preordered vector spaces. In: Internationale Tagung Mathematische Optimierung — Theorie und Anwendungen, Eisenach, pp 58–61

  • Isermann H (1982) Linear lexicographic optimization. OR Spektrum 4:223–228

    Google Scholar 

  • Luptácik M, Turnovec F (1990) Lexicographic geometric programming. Eur J Oper Res, to appear

  • Martínez-Legaz JE (1984) Lexicographical order, inequality systems and optimization. In: Thoft-Christensen P (ed) System modelling and optimization. Springer, Berlin Heidelberg New York, pp 203–212

    Google Scholar 

  • Martínez-Legaz JE (1988) Lexicographical order and duality in multiobjective programming. Eur J Oper Res 33:342–348

    Google Scholar 

  • Martínez-Legaz JE, Singer I (1987) Surrogate duality for vector optimization. Numer Funct Anal and Optimiz 9:547–568

    Google Scholar 

  • Martínez-Legaz JE, Singer I (1990) Lexicographical order, lexicographical index and linear operators. Linear Algebra Appl 128:65–95

    Google Scholar 

  • Sawaragi Y, Nakayama H, Tanino T (1985) Theory of multiobjective optimization. Mathematics in Science and Engineering. Academic Press, Orlando

    Google Scholar 

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Authors and Affiliations

  1. Universidad de Barcelona, Spanien

    J. E. Martínez-Legaz

Authors
  1. J. E. Martínez-Legaz
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Additional information

Financial support from the Dirección General de Investigación Cientifica y Técnica (DGICYT), under project PS89-0058, is gratefully acknowledged.

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Martínez-Legaz, J.E. Characterizations of efficient solutions under polyhedrality assumptions. ZOR - Methods and Models of Operations Research 35, 221–230 (1991). https://doi.org/10.1007/BF01415908

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