@article{ZVMMF_1992_32_8_a6,
author = {I. L. Averbakh},
title = {Group-theoretic method of decomposition methods in integer linear programming},
journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
pages = {1229--1243},
year = {1992},
volume = {32},
number = {8},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZVMMF_1992_32_8_a6/}
}
TY - JOUR AU - I. L. Averbakh TI - Group-theoretic method of decomposition methods in integer linear programming JO - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki PY - 1992 SP - 1229 EP - 1243 VL - 32 IS - 8 UR - http://geodesic.mathdoc.fr/item/ZVMMF_1992_32_8_a6/ LA - ru ID - ZVMMF_1992_32_8_a6 ER -
I. L. Averbakh. Group-theoretic method of decomposition methods in integer linear programming. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 32 (1992) no. 8, pp. 1229-1243. http://geodesic.mathdoc.fr/item/ZVMMF_1992_32_8_a6/
[1] Averbakh I. L., Tsurkov V. I., “Tselochislennye optimizatsionnye modeli blochnogo tipa”, Matem. modelirovanie, 2:2 (1990), 39–57 | MR | Zbl
[2] Pozdnyakov Yu. M., “Dekompozitsionnaya skhema resheniya zadach tselochislennogo lineinogo programmirovaniya”, Zh. vychisl. matem. i matem. fiz., 22:1 (1982), 57–67 | MR | Zbl
[3] Sweeney D., Murphy R., “A method of decomposition for integer programs”, Operat. Res., 27:6 (1979), 1128–1141 | DOI | MR | Zbl
[4] Averbakh I. L., “Kombinirovannaya dekompozitsiya v blochnykh zadachakh tselochislennogo lineinogo programmirovaniya”, Avtomatika i telemekhan., 1990, no. 7, 108–115 | MR | Zbl
[5] Lebedev S. S., “Tselochislennoe programmirovanie i mnozhiteli Lagranzha”, Ekonomika i matem. metody, 10:3 (1974), 592–610 | MR
[6] Averbakh I. L., “Iterativnyi metod dekompozitsii v odnoetapnykh zadachakh ctoxasticheskogo tselochislennogo programmirovaniya”, Zh. vychisl. matem. i matem. fiz., 30:10 (1990), 1467–1476 | MR
[7] Averbakh I.L̇., “Iterativnyi metod resheniya dvukhetapnykh diskretnykh zadach stokhasticheskogo programmirovaniya s additivno razdelyaemymi peremennymi”, Zh. vychisl. matem. i matem. fiz., 31:6 (1991), 810–818 | MR
[8] Shapiro J., Mathematical programming: structures and algorithms, J. Wiley and Sons, N. Y., 1979 | MR
[9] Shlyk V. A., “O teoretiko-gruppovom podkhode v tselochislennom lineinom programmirovanii”, Izv. AN SSSR. Tekhn. kibernetika, 1988, no. 1, 94–105
[10] Weil R. L., Kettler P. C., “Rearranging matrices into block-angular form for decomposition (and other) algorithms”, Manag. Sci., 18:1 (1971), 98–108 | DOI | MR | Zbl
[11] Glover F., Klingman D., “Layering strategies for creating exploitable structure in linear and integer programs”, Math. Program., 40:2 (1988), 165–181 | DOI | MR | Zbl
[12] Guignard M., Kim S., “Lagrangean decomposition: a model yielding stronger Lagrangean bound”, Math. Program., 39:2 (1987), 215–228 | DOI | MR | Zbl
[13] Bell D., Shapiro J., “A convergent duality theory for integer programming”, Operat Res., 25:3 (1977), 419–434 | DOI | MR | Zbl
[14] Trishin V. H., “Modifitsirovannyi algoritm gruppovoi minimizatsii s ispolzovaniem opornykh elementov”, Zh. vychisl. matem. i matem. fiz., 22:3 (1982), 593–598 | MR | Zbl
[15] Lawler E. L., “A procedure for computing the $k$ best solutions to discrete optimization problems and its application to the shortest path problem”, Manag. Sci., 18 (1972), 401–405 | DOI | MR | Zbl
[16] Wolsey L., “A number theoretic reformulation and decomposition method for integer programming”, Discrete Math., 7 (1974), 393–403 | DOI | MR | Zbl
[17] Minu M., Matematicheskoe programmirovanie, Nauka, M., 1990 | MR