On Minkowski metric and weighted Tchebyshev norm in vector optimization

C. J. Goh, Xiaoqi Yang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

1 Citation (Scopus)

Abstract

The typical approach in solving vector optimization problems is to scalarize the vector cost function into a single cost function by means of some utility or value function. A very large class of utility function is given by the Minkowski's metric proposed by Charnes and Cooper in the context of goal programming. This includes the special case of linear scalarization and the weighted Tchebyshev norm. We shall furnish a rigorous justification that there is no equivalent relationship between the general vector optimization problem and scalarized optimization problems using any Minkowski's metric utility function. Furthermore, we also show that the weighted Tchebyshev norm is, in some sense, the best amongst the class of Minkowski's metric utility functions since it is the only scalarization method which yields an equivalence relation between the weak vector optimization problem and a set of scalar optimization problems, without any convexity assumption. Published under license under the Gordon and Breach Science Publishers imprint.
Original languageEnglish
Pages (from-to)353-365
Number of pages13
JournalOptimization
Volume43
Issue number4
DOIs
Publication statusPublished - 1 Jan 1998
Externally publishedYes

Keywords

  • Minkowski metric
  • Monotone functions
  • Scalarization methods
  • Tchebyshev norm
  • Vector optimization

ASJC Scopus subject areas

  • Control and Optimization
  • Management Science and Operations Research
  • Applied Mathematics

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