Operations-Research-Spektrum

, Volume 16, Issue 1, pp 53–58 | Cite as

Kolmogorov-conditions for vectorial approximation problems

  • Gert Wanka
Theoretical Papers

Abstract

A general vectorial best approximation problem in linear and locally convex topological spaces, respectively, is considered. The approximation is based on socalled vectorial norms. For efficient, weakly efficient and strongly efficient solutions sufficient optimality conditions which can be interpreted as generalized Kolmogorov-conditions are obtained in vectorial as well as scalarized form.

Key words

Vectorial approximation optimality conditions vectorial norms efficient points multicriterial optimization 

Zusammenfassung

Untersucht wird ein allgemeines vektorielles Bestapproximationsproblem in linearen bzw. lokalkonvexen topologischen Räumen. Die Approximation wird im Sinne sogenannter vektorieller Normen betrachtet. Es werden für effiziente, schwach effiziente und streng minimale Lösungen hinreichende Optimalitätsbedingungen angegeben. Diese können als verallgemeinerte Kolmogorov Bedingungen interpretiert werden.

Schlüsselwörter

Vektorielle Approximation Optimalitätsbedingungen vektorielle Normen effiziente Punkte multikriterielle Optimierung 

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Copyright information

© Springer-Verlag 1994

Authors and Affiliations

  • Gert Wanka
    • 1
  1. 1.Fachbereich MathematikTechnische Universität Chemnitz-ZwickauChemnitzDeutschland

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