Computing minimal elements of finite families of sets w.r.t. preorder relations in set optimization

Research output: Contribution to journal › Article › Research › peer review

Authors

  • Christian Günther
  • Elisabeth Köbis
  • Nicolae Popovici

External Research Organisations

  • Martin Luther University Halle-Wittenberg
  • Babeş-Bolyai University (UBB)
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Details

Original languageEnglish
Pages (from-to)131-144
Number of pages14
JournalJournal of Applied and Numerical Optimization
Volume1
Issue number2
Early online date31 Aug 2019
Publication statusPublished - 2019
Externally publishedYes

Abstract

We propose new algorithms for computing all minimal elements of a nonempty finite family of sets in a real linear space, with respect to a preorder relation defined on the power set of that space. These algorithms are based on a set-valued counterpart of the well-known Graef-Younes reduction procedure, originally conceived for vector optimization. One of our algorithms consists of two subsequent (forward-backward) reduction procedures, similarly to the classical Jahn-Graef-Younes method. Another algorithm involves a pre-sorting procedure with respect to a strongly increasing real-valued function, followed by a single (forward) reduction procedure. Numerical experiments in MATLAB allow us to compare our algorithms for special test families of line segments with respect to `-type, u-type and s-type preorder relations, currently used in set optimization.

Keywords

    External stability, Graef-Younes reduction method, Minimal element, Preorder relation, Sorting scalar function

ASJC Scopus subject areas

Cite this

Computing minimal elements of finite families of sets w.r.t. preorder relations in set optimization. / Günther, Christian; Köbis, Elisabeth; Popovici, Nicolae.
In: Journal of Applied and Numerical Optimization, Vol. 1, No. 2, 2019, p. 131-144.

Research output: Contribution to journal › Article › Research › peer review

Günther, C, Köbis, E & Popovici, N 2019, 'Computing minimal elements of finite families of sets w.r.t. preorder relations in set optimization', Journal of Applied and Numerical Optimization, vol. 1, no. 2, pp. 131-144. https://doi.org/10.23952/jano.1.2019.2.04
Günther, C., Köbis, E., & Popovici, N. (2019). Computing minimal elements of finite families of sets w.r.t. preorder relations in set optimization. Journal of Applied and Numerical Optimization, 1(2), 131-144. https://doi.org/10.23952/jano.1.2019.2.04
Günther C, Köbis E, Popovici N. Computing minimal elements of finite families of sets w.r.t. preorder relations in set optimization. Journal of Applied and Numerical Optimization. 2019;1(2):131-144. Epub 2019 Aug 31. doi: 10.23952/jano.1.2019.2.04
Günther, Christian ; Köbis, Elisabeth ; Popovici, Nicolae. / Computing minimal elements of finite families of sets w.r.t. preorder relations in set optimization. In: Journal of Applied and Numerical Optimization. 2019 ; Vol. 1, No. 2. pp. 131-144.
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