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Operations-Research-Spektrum

, Volume 16, Issue 4, pp 249–254 | Cite as

Multicriteria fractional programming — an approach by means of conjugate functions

  • E. Ohlendorf
  • Ch. Tammer
Decision Theory

Abstract

This paper deals with multicriteria fractional problems. Since this problems in general are not convex, the basic problem will be transformed into a convex optimization problem by using an extension of the conception of Dinkelbach to vector optimization. It will be formulated a dual problem to the transformed optimization problem, where conjugate functions are used. There will be proved strong and converse duality theorems with conclusions to basic fractional problem.

Key words

Fractional programming Dinkelbach-algorithm duality conjugate functions 

Zusammenfassung

In diesem Artikel wird ein Quotientenvektoroptimierungsproblem betrachtet. Da solche Probleme im allgemeinen nicht konvex sind, wird das Ausgangsproblem mit Hilfe des Ansatzes von Dinkelbach in ein konvexes Optimierungsproblem transformiert. Zum transformierten Problem wird mit Hilfe von verallgemeinerten Fenchel-konjugierten Funktionen ein duales Problem formuliert. Entsprechende Dualitätssätze werden bewiesen und Rückschlüsse auf die Lösung der Ausgangsaufgabe gezogen.

Schlüsselwörter

Quotientenoptimierung Dinkelbachansatz Dualität konjugierte Funktionen 

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Copyright information

© Springer-Verlag 1994

Authors and Affiliations

  • E. Ohlendorf
    • 1
  • Ch. Tammer
    • 1
  1. 1.Department of Mathematics and Informatics, Institute for Optimization and StochasticsMartin-Luther-University HalleHalle/SaaleGermany

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