Geodesic
“Higher-order” necessary optimality conditions in a linear maximin problem with coupled variables
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 50 (2010) no. 6, pp. 1017-1022 
A. R. Mamatov. “Higher-order” necessary optimality conditions in a linear maximin problem with coupled variables. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 50 (2010) no. 6, pp. 1017-1022. http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_6_a3/
@article{ZVMMF_2010_50_6_a3,
     author = {A. R. Mamatov},
     title = {{\textquotedblleft}Higher-order{\textquotedblright} necessary optimality conditions in a linear maximin problem with coupled variables},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1017--1022},
     year = {2010},
     volume = {50},
     number = {6},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_6_a3/}
}
TY  - JOUR
AU  - A. R. Mamatov
TI  - “Higher-order” necessary optimality conditions in a linear maximin problem with coupled variables
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2010
SP  - 1017
EP  - 1022
VL  - 50
IS  - 6
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_6_a3/
LA  - ru
ID  - ZVMMF_2010_50_6_a3
ER  - 
%0 Journal Article
%A A. R. Mamatov
%T “Higher-order” necessary optimality conditions in a linear maximin problem with coupled variables
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2010
%P 1017-1022
%V 50
%N 6
%U http://geodesic.mathdoc.fr/item/ZVMMF_2010_50_6_a3/
%G ru
%F ZVMMF_2010_50_6_a3

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

For a linear maxmin problem with equality constraints, a theorem is proved that provides a basis for constructing an efficient algorithm for its solution.

[1] Golshtein E. G., Teoriya dvoistvennosti v matematicheskom programmirovanii i ee prilozheniya, Nauka, M., 1971 | MR

[2] Gabasov R., Kirillova F. M., Tyatyushkin A. I., Konstruktivnye metody optimizatsii, v. 1, Lineinye zadachi, Universitetskoe, Minsk, 1984 | MR

[3] Ivanilov Yu. P., “Dvoistvennye poluigry”, Izv. AN SSSR. Tekhn. kibernetika, 1972, no. 4, 3–9 | MR | Zbl

[4] Falk J. E., “Linear max-min problem”, Math. Program., 5:2 (1973), 169–188 | DOI | MR | Zbl

[5] Mamatov A. R., “Dvoistvennyi algoritm vychisleniya lokalnogo optimuma lineinoi maksiminnoi zadachi so svyazannymi peremennymi”, Uzbekskii zh. probl. informatiki i energetiki, 2001, no. 1

[6] Mamatov A. R., “K teorii dvoistvennosti lineinykh maksiminnykh zadach so svyazannymi peremennymi”, Sibirskii zhurnal vychisl. matem., 10:2 (2007), 181–187 | MR

[7] Mamatov A. R., “Ob odnoi igrovoi zadache so svyazannymi peremennymi”, Dokl. AN RUz., 1993, no. 7, 7–13

[8] Fedorov V. V., Chislennye metody maksimina, Nauka, M., 1979 | MR

[9] Azizov I., Konechnyi algoritm resheniya lineinoi maksiminnoi zadachi so svyazannymi peremennymi i rezultaty chislennogo eksperimenta, Preprint 18(203), In-t matem. AN BSSR, Minsk, 1984, 20 pp.

[10] Lozovanu D. D., “Maksiminnye zadachi so svyazannymi peremennymi i ikh primeneniya k issledovaniyu i resheniyu tsiklicheskikh igr”, Izv. AN SSR. Moldova. Matematika, 1990, no. 2, 22–29 | MR | Zbl

[11] Mamatov A. R., “Algoritm resheniya lineinoi maksiminnoi zadachi so svyazannymi peremennymi”, Zh. vychisl. matem. i matem. fiz., 45:6 (2005), 1044–1047 | MR | Zbl

[12] Mamatov A. R., “Algoritm resheniya odnoi igry dvukh lits s peredachei informatsii”, Zh. vychisl. matem. i matem. fiz., 46:10 (2006), 1784–1789 | MR