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On Scalarizing Method in Vector Optimization

  • The Luc Dinh
Part of the Lecture Notes in Economics and Mathematical Systems book series (LNE, volume 273)

Abstract

Let K be a closed,convex and pointed cone with a nonempty interior int K in an n-dimensional Euclidean space Rn.The cone induces preference orders in the space as follows: .a,b∈Rn,
$$ \begin{gathered} a \geqslant b\quad if\quad a - b \in K \hfill \\ a \leqslant b\quad if\quad a - b \in K\backslash \left\{ 0 \right\} \hfill \\ a > b\quad if\quad a - b \in \operatorname{int} K \hfill \\ \end{gathered} $$

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References

  1. Jahn, J.(1984). Scalarization in vector optimization, Mathematical Programming 29,203–218.CrossRefGoogle Scholar
  2. Wierzbicki, P.(1985).0n the completeness and constructiveness of parametric characterizations to vector optimization problems International Workshop on large-scale modelling and interactive decision analysis,Wartburg-GDR,reprint.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1986

Authors and Affiliations

  • The Luc Dinh
    • 1
  1. 1.VietNam

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