Geodesic
Stability analysis of the efficient solution to a~vector problem of a~maximum cut
Diskretnyj analiz i issledovanie operacij, Tome 20 (2013) no. 4, pp. 27-35.

Voir la notice de l'article provenant de la source Math-Net.Ru

We consider a MAX-CUT multicriteria problem. A formula for the stability radius of effective solutions is obtained in the case of the Hölder norm in the parameter space. Bibliogr. 18.
Keywords: multi-objectiveness, effective cut, stability radius, Hölder norm. 
@article{DA_2013_20_4_a2,
     author = {V. A. Emelichev and K. G. Kuzmin},
     title = {Stability analysis of the efficient solution to a~vector problem of a~maximum cut},
     journal = {Diskretnyj analiz i issledovanie operacij},
     pages = {27--35},
     publisher = {mathdoc},
     volume = {20},
     number = {4},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DA_2013_20_4_a2/}
}
TY  - JOUR
AU  - V. A. Emelichev
AU  - K. G. Kuzmin
TI  - Stability analysis of the efficient solution to a~vector problem of a~maximum cut
JO  - Diskretnyj analiz i issledovanie operacij
PY  - 2013
SP  - 27
EP  - 35
VL  - 20
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DA_2013_20_4_a2/
LA  - ru
ID  - DA_2013_20_4_a2
ER  - 
%0 Journal Article
%A V. A. Emelichev
%A K. G. Kuzmin
%T Stability analysis of the efficient solution to a~vector problem of a~maximum cut
%J Diskretnyj analiz i issledovanie operacij
%D 2013
%P 27-35
%V 20
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DA_2013_20_4_a2/
%G ru
%F DA_2013_20_4_a2
V. A. Emelichev; K. G. Kuzmin. Stability analysis of the efficient solution to a~vector problem of a~maximum cut. Diskretnyj analiz i issledovanie operacij, Tome 20 (2013) no. 4, pp. 27-35. http://geodesic.mathdoc.fr/item/DA_2013_20_4_a2/

[1] Vodennikov A. G., Emelichev V. A., Kuzmin K. G., “Ob odnom tipe ustoichivosti vektornoi kombinatornoi zadachi razmescheniya”, Diskret. analiz i issled. operatsii. Ser. 2, 14:2 (2007), 32–40 | MR | Zbl

[2] Geri M., Dzhonson D., Vychislitelnye mashiny i trudnoreshaemye zadachi, Mir, M., 1982, 416 pp. | MR

[3] Emelichev V. A., Karpuk A. V., Kuzmin K. G., “O kvaziustoichivosti leksikograficheskoi minimaksnoi kombinatornoi zadachi s raspadayuschimisya peremennymi”, Diskret. analiz i issled. operatsii, 17:3 (2010), 32–45 | MR | Zbl

[4] Emelichev V. A., Kuzmin K. G., “Analiz chuvstvitelnosti effektivnogo resheniya vektornoi bulevoi zadachi minimizatsii proektsii lineinykh funktsii na $\mathbb R_+$ i $\mathbb R_-$”, Diskret. analiz i issled. operatsii. Ser. 2, 12:2 (2005), 24–43 | MR | Zbl

[5] Emelichev V. A., Kuzmin K. G., “O radiuse ustoichivosti effektivnogo resheniya vektornoi zadachi tselochislennogo lineinogo programmirovaniya v metrike Gëldera”, Kibernetika i sistem. analiz, 2006, no. 4, 175–181 | Zbl

[6] Emelichev V. A., Kuzmin K. G., “Ob ustoichivosti effektivnykh reshenii mnogokriterialnoi zadachi o maksimalnom razreze grafa”, Mat. Vseukr. nauchn. seminara “Kombinatorna optimizatsiya ta nechitki mnozhini”, KONeM–2011 (Poltava, Ukraina, 26–27 avgusta 2011 g.), 39–41

[7] Emelichev V. A., Kuzmin K. G., “Obschii podkhod k issledovaniyu ustoichivosti pareto-optimalnogo resheniya vektornoi zadachi tselochislennogo lineinogo programmirovaniya”, Diskret. matematika, 19:3 (2007), 79–83 | DOI | MR | Zbl

[8] Emelichev V. A., Kuzmin K. G., “Postoptimalnyi analiz mnogokriterialnoi zadachi o maksimalnom razreze grafa”, Mat. 2-i mezhdunar. nauch.-prakt. konf. “Veb-programmirovanie i internet tekhnologii WebConf2012” (Minsk, 5–7 iyunya 2012 g.), 67

[9] Emelichev V. A., Melnikov O. I., Sarvanov V. I., Tyshkevich R. I., Lektsii po teorii grafov, 3-e izd., Librokom, M., 2013, 392 pp.

[10] Zykov A. A., Osnovy teorii grafov, Vuz. kn., M., 2004, 663 pp.

[11] Khardi G., Littlvud Dzh. E., Polia G., Neravenstva, LKI, M., 2008, 456 pp.

[12] Shilo V. P., Shilo O. V., “Reshenie zadachi o maksimalnom razreze grafa metodom globalnogo ravnovesnogo poiska”, Kibernetika i sistem. analiz, 2010, no. 5, 68–79 | MR

[13] Barahona F., Grötschel M., Jünger M., Reinelt G., “An application of combinatorial optimization to statistical physics and circuit layout design”, Oper. Res., 36:3 (1988), 493–513 | DOI | MR | Zbl

[14] Burer S., Monteiro R. D. C., Zhang Y., “Rank-two relaxation heuristics for MAX-CUT and other binary quadratic programs”, SIAM J. Optim., 12 (2001), 503–521 | DOI | MR | Zbl

[15] Chang K. C., Du D. H.-C., “Efficient algorithms for layer assignment problem”, IEEE Trans. Computer-Aided Des. Integrated Circuits Syst., 6 (1987), 67–78 | DOI

[16] Emelichev V., Podkopaev D., “Quantitative stability analysis for vector problems of 0-1 programming”, Discrete Optim., 7:1–2 (2010), 48–63 | DOI | MR | Zbl

[17] Pardalos P., Prokopyev O., Shylo O., Shylo V., “Global equilibrium search applied to the unconstrained binary quadratic optimization problem”, Optim. Methods Softw., 23 (2008), 129–140 | DOI | MR | Zbl

[18] Poljac S., Tuza Z., “Maximum cuts and large bipartite subgraphs”, DIMACS Ser. Discrete Math. Theor. Comput. Sci., 20 (1995), 181–244 | MR