On the hierarchical structure of Pareto critical sets

  • Bennet GebkenEmail author
  • Sebastian Peitz
  • Michael Dellnitz


In this article we show that the boundary of the Pareto critical set of an unconstrained multiobjective optimization problem (MOP) consists of Pareto critical points of subproblems where only a subset of the set of objective functions is taken into account. If the Pareto critical set is completely described by its boundary (e.g., if we have more objective functions than dimensions in decision space), then this can be used to efficiently solve the MOP by solving a number of MOPs with fewer objective functions. If this is not the case, the results can still give insight into the structure of the Pareto critical set.


Multiobjective optimization Many-objective optimization Pareto set Pareto critical set 



This research was funded by the DFG Priority Programme 1962 ”Non-smooth and Com-plementarity-based Distributed Parameter Systems”.


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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • Bennet Gebken
    • 1
    Email author
  • Sebastian Peitz
    • 1
  • Michael Dellnitz
    • 1
  1. 1.Chair of Applied MathematicsPaderborn UniversityPaderbornGermany

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