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Comparison of Existence Results for Efficient Points

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Abstract

Existence results of maximal points with respect to general binary relations were stated by Hazen and Morin (Ref. 1) and by Gajek and Zagrodny (Ref. 2). In this paper, we point out that the natural framework for this problem is that of transitive and reflexive relations (preorders). The aim of this paper is to discuss existence results for maximal points with respect to general transitive relations in such a way that, when considering them for preorders defined by convex cones, we are able to recover most known existence results for efficient points; the quasi-totality of them, with their (short) proofs, is presented, too.

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Authors and Affiliations

  1. Département de Mathématiques, Technopôle de Château Gombert, Université de Provence, Marseille, France

    Y. Sonntag (Associate Professor)

  2. Faculty of Mathematics, University Al. I. Cuza, Iaşi, Romania

    C. Zalinescu (Professor)

Authors
  1. Y. Sonntag
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  2. C. Zalinescu
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Sonntag, Y., Zalinescu, C. Comparison of Existence Results for Efficient Points. Journal of Optimization Theory and Applications 105, 161–188 (2000). https://doi.org/10.1023/A:1004670229860

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