Value functions, domination cones and proper efficiency in multicriteria optimization

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Abstract

In the absence of a clear "objective" value function, it is still possible in many cases to construct a domination cone according to which efficient (nondominated) solutions can be found. The relations between value functions and domination cones and between efficiency and optimality are analyzed here. We show that such cones must be convex, strictly supported and, frequently, closed as well. Furthermore, in most applications "potential" optimal solutions are equivalent to properly efficient points. These solutions can often be produced by maximizing with respect to a class of concave functions or, under convexity conditions, a class of affine functions.

Original languageEnglish
Pages (from-to)205-217
Number of pages13
JournalMathematical Programming
Volume46
Issue number1-3
DOIs
StatePublished - Jan 1990

Keywords

  • Multicriteria optimization
  • convex analysis
  • proper efficiency
  • value theory

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