Optimisation d’une fonction linéaire sur l’ensemble des solutions efficaces d’un problème multicritère quadratique convexe
Belkeziz, K. ; Metrane, A.
Annales mathématiques Blaise Pascal, Tome 11 (2004), p. 19-33 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU)

Dans ce papier, nous caractérisons l’ensemble des points efficients d’un problème de programmation multicritère quadratique convexe. Nous ramenons ainsi le problème de la minimisation d’une fonction linéaire sur l’ensemble des points efficients à la résolution d’un problème de programmation fractionnaire.

@article{AMBP_2004__11_1_19_0,
     author = {Belkeziz, K. and Metrane, A.},
     title = {Optimisation d'une fonction lin\'eaire sur l'ensemble des solutions efficaces d'un probl\`eme multicrit\`ere quadratique convexe},
     journal = {Annales math\'ematiques Blaise Pascal},
     volume = {11},
     year = {2004},
     pages = {19-33},
     doi = {10.5802/ambp.182},
     zbl = {02207855},
     mrnumber = {2077235},
     zbl = {1132.90014},
     language = {fr},
     url = {http://dml.mathdoc.fr/item/AMBP_2004__11_1_19_0}
}

Belkeziz, K.; Metrane, A. Optimisation d’une fonction linéaire sur l’ensemble des solutions efficaces d’un problème multicritère quadratique convexe. Annales mathématiques Blaise Pascal, Tome 11 (2004) pp. 19-33. doi : 10.5802/ambp.182. http://gdmltest.u-ga.fr/item/AMBP_2004__11_1_19_0/

[1] A. V. Fiacco, G. P. Mccormick Nonlinear Programming, Sequential unconstrained minimization techniques, Classics in Applied Mathematics (1990) | MR 1058438 | Zbl 0713.90043

[2] Benson, H. P. Efficiency and proper efficiency in vector maximization with respect to cones, Journal of Mathematical Analysis and Applications, Tome 93 (1983), pp. 273-289 | Article | MR 699713 | Zbl 0519.90080

[3] Benson, H. P. Optimization over the Efficient Set, Journal of Mathematical Analysis and Applications, Tome 98 (1984), pp. 562-580 | Article | MR 730527 | Zbl 0534.90077

[4] Benson, H. P. An algorithm for optimizing over the weakly-efficient set, European Journal of Operational Research, Tome 25 (1986), pp. 192-199 | Article | MR 841149 | Zbl 0594.90082

[5] Fulop, J. A Cutting Plane Method for Linear Optimization over the Efficient Set, Generalized Convexity, Edited by S. Komlosi, T. Rapcsak, and S. Schaible (1994), pp. 374-385 | MR 1272281

[6] Gal, T. A general method for determing the set of all efficient solutions to a linear vector-maximum problem, European Journal of Operational Research, Tome 1 (1977), pp. 307-322 | Article | MR 462565 | Zbl 0374.90044

[7] Geoffrion, A. M. Proper efficiency and the theory of vector maximization, Journal of Mathematical Analysis and Applications, Tome 22 (1968), pp. 618-630 | Article | MR 229453 | Zbl 0181.22806

[8] Isermann, H. The enumeration of the set of all efficient solutions for all a linear multiple objective program, Operationel Research Quarterly, Tome 28 (1977), pp. 711-725 | Article | Zbl 0372.90086

[9] J. G Ecker, N. S. Hegner; Kouada, I. A. Generating all maximal efficient faces for multiple linear programs, Journal of optimization Theory and applications, Tome 30 (1980), pp. 353-381 | Article | MR 567792 | Zbl 0393.90087

[10] Luc, D. T. Theory of Vector Optimization, Springer-verlag, Berlin Heidelberg New-York London Paris Tokyo (1989) | MR 1116766

[11] P. T. Thach, H. Konno; Yokota, D. A Dual Approch to a Minimization on the Set of Pareto-Optimal Solutions, Working Paper, Institute of Human and Social Sciences, Tokyo Institute of Technology,Tokyo, Japan (1994)

[12] Tamara, K.; Miura, S. On linear vector maximization problems, Journal of the Operations Research Society of Japan, Tome 20 (1977), pp. 139-149 | MR 452661 | Zbl 0372.90087