×

On five types of stability of the lexicographic variant of the combinatorial bottleneck problem. (English. Russian original) Zbl 1261.90043

Discrete Math. Appl. 19, No. 4, 337-348 (2009); translation from Diskretn. Mat. 21, No. 3, 3-13 (2009).
Summary: We consider the combinatorial vector minimax problem with ordered criteria. We formulate necessary and sufficient conditions for the five known types of stability of the problem which describe the behaviour of the lexicographic set with respect to perturbations of the initial data for the vector criterion.

MSC:

90C27 Combinatorial optimization
90C31 Sensitivity, stability, parametric optimization
Full Text: DOI

References:

[1] Lebedeva T. T., Cybern. Syst. Anal. 40 pp 52– (2004) · Zbl 1066.90118 · doi:10.1023/B:CASA.0000028099.91014.d8
[2] Lebedeva T. T., Cybern. Syst. Anal. 41 pp 551– (2005) · Zbl 1098.90066 · doi:10.1007/s10559-005-0090-z
[3] Lebedeva T. T., Cybern. Syst. Anal. 42 pp 667– (2006) · Zbl 1119.90055 · doi:10.1007/s10559-006-0104-5
[4] Lebedeva T. T., Cybern. Syst. Anal. 44 pp 429– (2008) · Zbl 1143.90360 · doi:10.1007/s10559-008-9017-9
[5] Emelichev V. A., Cybern. Syst. Anal. 43 pp 759– (2007) · Zbl 1144.90014 · doi:10.1007/s10559-007-0100-4
[6] Emelichev V. A., Kibernet. Sistem. Anal. 44 (3) pp 103– (2008)
[7] Emelichev V. A., Discrete Math. Appl. 5 pp 93– (1995) · Zbl 0839.90095 · doi:10.1515/dma.1995.5.2.93
[8] Sotskov Yu. N., Discrete Appl. Math. 58 (2) pp 169– (1995) · Zbl 0833.90098 · doi:10.1016/0166-218X(93)E0126-J
[9] Emelichev V. A., Discrete Math. Appl. 8 pp 135– (1998) · Zbl 0997.90070 · doi:10.1515/dma.1998.8.2.135
[10] Emelichev V. A., Discrete Math. Appl. 8 pp 383– (1998) · Zbl 0966.90066 · doi:10.1515/dma.1998.8.4.383
[11] Emelichev V. A., Russian Math. 42 (12) pp 9– (1998)
[12] Emelichev V. A., Optimization 51 (4) pp 645– (2002) · Zbl 1109.90325 · doi:10.1080/0233193021000030760
[13] Emelichev V. A., Comput. Sci. J. Mold. 7 (1) pp 105– (1999)
[14] Gordeev E. N., Comput. Math. Math. Phys. 33 pp 1229– (1993)
[15] Gordeev E. N., Comput. Math. Math. Phys. 36 pp 53– (1996)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.