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multicriteria optimization; (proper) Pareto optimality; scalarization; $L_p$-norm
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.
[1] Ehrgott M.: Multicriteria Optimization. Springer–Verlag, Berlin 2000. Second edition Springer, Berlin 2005 MR 2143243 | Zbl 1132.90001
[2] Figueira J., Greco, S., Ehrgott M.: Multiple criteria decision analysis: State of the art surveys. Kluwer Academic Publishers, Boston – Dordrecht – London 2005 Zbl 1060.90002
[3] Franklin J.: Methods of Mathematical Economics. Linear and Nonlinear Programming. Fixed-Point Theorems. Springer, New York 1980 MR 0602694 | Zbl 1075.90001
[4] Geoffrion A. M.: Proper efficiency and the theory of vector maximization. J. Math. Anal. Appl. 22 (1968) 618–630 MR 0229453 | Zbl 0181.22806
[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 MR 1831852
[7] Romero C.: Multi-objective and goal-programming approaches as a distance function model. J. Operat. Res. Soc. 36 (1985), 3, 249–251 Zbl 0555.90093
[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 Zbl 0937.90048
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