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On several concepts for ɛ-efficiency

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Abstract

We introduce two new concepts forɛ-efficiency and investigate these and some known concepts under the following aspects: (1) What are the relationships between the efficient and theɛ-efficient point set? (2) If the sequence (v ɛ) ofɛ-efficient points converges forε → 0, is the limit efficient, or weakly efficient? (3) Can the distance between theɛ-efficient and the efficient point set be estimated in terms ofε?

Zusammenfassung

Wir führen zwei neue Konzepte fürɛ-Effizienz ein und untersuchen diese und einige bekannte Konzepte unter folgenden Gesichtspunkten: (1) Wie sind die Beziehungen zwischen den Mengen der effizienten und derɛ-effizienten Punkte? (2) Wenn eine Folge (v ɛ) vonɛ-effizienten Punkten fürε → 0 konvergiert, welche Aussagen können über den Limes gemacht werden (effizient, schwach effizient, ...)? (3) Kann der Abstand zwischen den Mengen derɛ-effizienten und effizienten Punkte bezüglichε abgeschätzt werden?

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Authors and Affiliations

  1. Fachbereich Mathematik, Johann-Wolfgang-Goethe-Universität, Robert-Mayer-Strasse 6-10, D-60325, Frankfurt/Main, Germany

    Siegfried Helbig

  2. Institute for Mathematics, Bulgarian Academy of Sciences, ul. Akad. G. Bontchev 8, BG-1113, Sofia, Bulgaria

    Darinka Pateva

Authors
  1. Siegfried Helbig
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  2. Darinka Pateva
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Partially supported by the Ministry of Education and Science of Bulgaria under Grand No. MM-21/91 and the Deutsche Forschungsgemeinschaft

Partially supported by the Ministry of Education and Science of Bulgaria under Grand No. MM-21/91

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Helbig, S., Pateva, D. On several concepts for ɛ-efficiency. OR Spektrum 16, 179–186 (1994). https://doi.org/10.1007/BF01720705

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