Details
| Original language | English |
|---|---|
| Pages (from-to) | 131-144 |
| Number of pages | 14 |
| Journal | Journal of Applied and Numerical Optimization |
| Volume | 1 |
| Issue number | 2 |
| Early online date | 31 Aug 2019 |
| Publication status | Published - 2019 |
| Externally published | Yes |
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
- Mathematics(all)
- Computational Mathematics
- Mathematics(all)
- Control and Optimization
- Mathematics(all)
- Numerical Analysis
- Mathematics(all)
- Modelling and Simulation
Cite this
- Standard
- Harvard
- Apa
- Vancouver
- BibTeX
- RIS
In: Journal of Applied and Numerical Optimization, Vol. 1, No. 2, 2019, p. 131-144.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Computing minimal elements of finite families of sets w.r.t. preorder relations in set optimization
AU - Günther, Christian
AU - Köbis, Elisabeth
AU - Popovici, Nicolae
N1 - Publisher Copyright: ©2019 Journal of Applied and Numerical Optimization
PY - 2019
Y1 - 2019
N2 - 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.
AB - 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.
KW - External stability
KW - Graef-Younes reduction method
KW - Minimal element
KW - Preorder relation
KW - Sorting scalar function
UR - http://www.scopus.com/inward/record.url?scp=85080144341&partnerID=8YFLogxK
U2 - 10.23952/jano.1.2019.2.04
DO - 10.23952/jano.1.2019.2.04
M3 - Article
VL - 1
SP - 131
EP - 144
JO - Journal of Applied and Numerical Optimization
JF - Journal of Applied and Numerical Optimization
SN - 2562-5527
IS - 2
ER -