Characterizing the nondominated set by separable functions

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Abstract

We present sufficient and necessary conditions for classes of separable (additive) functions to generate the set of nondominated outcomes in multicriteria optimization problems. The basic technique consists of convexifying the set of outcomes and then applying the standard characterization of a convex set by a class of linear functions. The conditions include the case when the set of feasible alternatives is convex and the criteria are convex-transformable. We show that the sum of powers and the sum of functions of exponents can generate the nondominated set for an arbitrary set of outcomes (under compactness conditions). We also discuss monotonicity, proper nondominance, uniqueness and connectedness of solutions, and weights and trade-offs with respect to these functions.

Original languageEnglish
Pages (from-to)423-444
Number of pages22
JournalJournal of Optimization Theory and Applications
Volume59
Issue number3
DOIs
StatePublished - Dec 1988

Keywords

  • Multicriteria optimization
  • Pareto sets
  • convex-transformable functions
  • separable functions

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