Weighted scalarization related to L p -metric and pareto optimality

Alexandra Šipošová

Kybernetika (2008)

  • Volume: 44, Issue: 5, page 731-740
  • ISSN: 0023-5954

Abstract

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Relations between (proper) Pareto optimality of solutions of multicriteria optimization problems and solutions of the minimization problems obtained by replacing the multiple criteria with L p -norm related functions (depending on the criteria, goals, and scaling factors) are investigated.

How to cite

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Šipošová, Alexandra. "Weighted scalarization related to $L_p$-metric and pareto optimality." Kybernetika 44.5 (2008): 731-740. <http://eudml.org/doc/33960>.

@article{Šipošová2008,
abstract = {Relations between (proper) Pareto optimality of solutions of multicriteria optimization problems and solutions of the minimization problems obtained by replacing the multiple criteria with $L_p$-norm related functions (depending on the criteria, goals, and scaling factors) are investigated.},
author = {Šipošová, Alexandra},
journal = {Kybernetika},
keywords = {multicriteria optimization; (proper) Pareto optimality; scalarization; $L_p$-norm; multicriteria optimization; (proper) Pareto optimality; scalarization; -norm},
language = {eng},
number = {5},
pages = {731-740},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Weighted scalarization related to $L_p$-metric and pareto optimality},
url = {http://eudml.org/doc/33960},
volume = {44},
year = {2008},
}

TY - JOUR
AU - Šipošová, Alexandra
TI - Weighted scalarization related to $L_p$-metric and pareto optimality
JO - Kybernetika
PY - 2008
PB - Institute of Information Theory and Automation AS CR
VL - 44
IS - 5
SP - 731
EP - 740
AB - Relations between (proper) Pareto optimality of solutions of multicriteria optimization problems and solutions of the minimization problems obtained by replacing the multiple criteria with $L_p$-norm related functions (depending on the criteria, goals, and scaling factors) are investigated.
LA - eng
KW - multicriteria optimization; (proper) Pareto optimality; scalarization; $L_p$-norm; multicriteria optimization; (proper) Pareto optimality; scalarization; -norm
UR - http://eudml.org/doc/33960
ER -

References

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  1. Ehrgott M., Multicriteria Optimization, Springer–Verlag, Berlin 2000. Second edition Springer, Berlin 2005 Zbl1132.90001MR2143243
  2. Figueira J., Greco, S., Ehrgott M., Multiple criteria decision analysis: State of the art surveys, Kluwer Academic Publishers, Boston – Dordrecht – London 2005 Zbl1060.90002
  3. Franklin J., Methods of Mathematical Economics, Linear and Nonlinear Programming. Fixed-Point Theorems. Springer, New York 1980 Zbl1075.90001MR0602694
  4. Geoffrion A. M., Proper efficiency and the theory of vector maximization, J. Math. Anal. Appl. 22 (1968) 618–630 (1968) Zbl0181.22806MR0229453
  5. Maňas M., Game Theory and its Applications (in Czech), SNTL, Prague 1991 
  6. Ogryczak W., Comments on properties of the minmax solution in goal programming, European J. Oper. Res. 132 (2001), 17–21 MR1831852
  7. Romero C., Multi-objective and goal-programming approaches as a distance function model, J. Operat. Res. Soc. 36 (1985), 3, 249–251 (1985) Zbl0555.90093
  8. Tamiz M., Jones, D., Romero C., Goal programming for decision making: An overview of the current state-of-the-art, European J. Oper. Res. 111 (1998), 569–581 (1998) Zbl0937.90048

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