Geodesic
On the quasistability of trajectory problems of vector optimization
Matematičeskie zametki, Tome 63 (1998) no. 1, pp. 21-27 
V. A. Emelichev; M. K. Kravtsov; D. P. Podkopaev. On the quasistability of trajectory problems of vector optimization. Matematičeskie zametki, Tome 63 (1998) no. 1, pp. 21-27. http://geodesic.mathdoc.fr/item/MZM_1998_63_1_a2/
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Voir la notice de l'article provenant de la source Math-Net.Ru

We consider quasistable multicriteria problems of discrete optimization on systems of subsets (trajectory problems). We single out the class of problems for which new Pareto optima can appear, while other optima for the problems do not disappear when the coefficients of the objective functions are slightly perturbed (in the Chebyshev metric). For the case of linear criteria (MINSUM), we obtain a formula for calculating the quasistability radius of the problem.

[1] Hadamard J., Sur les problèmes aux derivées partielles et leur signification partielle et leur signification physique, Bulletin, Princeton Univ., 1902

[2] Molodtsov D. A., Fedorov V. V., “Ustoichivost printsipov optimalnosti”, Sovremennoe sostoyanie teorii issledovaniya operatsii, Nauka, M., 1979, 236–263

[3] Matematicheskaya optimizatsiya: voprosy razreshimosti i ustoichivosti, eds. E. G. Belousov, B. Bank, Izd-vo MGU, M., 1986

[4] Dubov Yu. A., Travkin S. I., Yakimets V. N., Mnogokriterialnye modeli formirovaniya i vybora variantov sistem, Nauka, M., 1986

[5] Molodtsov D. A., Ustoichivost printsipov optimalnosti, Nauka, M., 1987 | Zbl

[6] Kozeratskaya L. N., Lebedeva T. T., Sergienko I. V., “Issledovanie ustoichivosti zadach diskretnoi optimizatsii”, Kibernetika i sistemnyi analiz, 1993, no. 3, 78–93 | MR | Zbl

[7] Sergienko I. V., Kozeratskaya L. N., Lebedeva T. T., Issledovanie ustoichivosti i parametricheskii analiz diskretnykh optimizatsionnykh zadach, Navukova dumka, Kiev, 1995

[8] Leontev V. K., “Ustoichivost zadachi kommivoyazhera”, ZhVMiMF, 15:5 (1975), 1298–1309 | MR | Zbl

[9] Sotskov Yu. N., Leontev V. K., Gordeev E. N., “Some concepts of stability analysis in combinatorial optimization”, Discrete Appl. Math., 58 (1995), 169–190 | DOI | MR | Zbl

[10] Gordeev E. N., Leontev V. K., “Obschii podkhod k issledovaniyu ustoichivosti reshenii v zadachakh diskretnoi optimizatsii”, ZhVMiMF, 36:1 (1996), 66–72 | MR | Zbl

[11] Emelichev V. A., Kravtsov M. K., “Ob ustoichivosti v traektornykh zadachakh vektornoi optimizatsii”, Kibernetika i sistemnyi analiz, 1995, no. 4, 137–143 | MR | Zbl

[12] Kozeratskaya L. N., Lebedeva T. T., Sergienko T. I., “Zadachi tselochislennogo programmirovaniya s vektornym kriteriem: parametricheskii analiz i issledovanie ustoichivosti”, Dokl. AN SSSR, 307:3 (1989), 527–529

[13] Podinovskii V. V., Nogin V. D., Pareto-optimalnye resheniya mnogokriterialnykh zadach, Nauka, M., 1982 | Zbl