Geodesic
Numerical solution of an equilibrium problem of based on the generalized level method
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 9, pp. 1588-1593 
E. G. Gol'shtein. Numerical solution of an equilibrium problem of based on the generalized level method. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 9, pp. 1588-1593. http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_9_a2/
@article{ZVMMF_2011_51_9_a2,
     author = {E. G. Gol'shtein},
     title = {Numerical solution of an equilibrium problem of based on the generalized level method},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1588--1593},
     year = {2011},
     volume = {51},
     number = {9},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_9_a2/}
}
TY  - JOUR
AU  - E. G. Gol'shtein
TI  - Numerical solution of an equilibrium problem of based on the generalized level method
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2011
SP  - 1588
EP  - 1593
VL  - 51
IS  - 9
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_9_a2/
LA  - ru
ID  - ZVMMF_2011_51_9_a2
ER  - 
%0 Journal Article
%A E. G. Gol'shtein
%T Numerical solution of an equilibrium problem of based on the generalized level method
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2011
%P 1588-1593
%V 51
%N 9
%U http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_9_a2/
%G ru
%F ZVMMF_2011_51_9_a2

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

An equilibrium problem is studied whose special case is finding a Nash point in a noncooperative multiperson game. A numerical algorithm for solving this problem is described. Conditions on the problem are stated under which an estimate is obtained for the convergence rate of the algorithm to a unique solution of the problem. The results are used for a numerical analysis of noncooperative games.

[1] Antipin A. S., “O skhodimosti i otsenkakh skorosti skhodimosti proksimalnykh metodov k nepodvizhnym tochkam ekstremalnykh otobrazhenii”, Zh. vychisl. matem. i matem. fiz., 35:5 (1995), 688–704 | MR | Zbl

[2] Antipin A. S., “Vychislenie nepodvizhnykh tochek ekstremalnykh otobrazhenii pri pomoschi metodov gradientnogo tipa”, Zh. vychisl. matem. i matem. fiz., 37:1 (1997), 42–53 | MR | Zbl

[3] Golshtein E. G., “Ob odnoi zadache ravnovesiya, svyazannoi s beskoalitsionnymi igrami”, Ekonomika i matem. metody, 45:4 (2009), 97–104

[4] Golshtein E. G., Nemirovskii A. S., Nesterov Yu. E., “Metod urovnei, ego oboboscheniya i prilozheniya”, Ekonomika i matem. metody, 31:3 (1995), 164–180

[5] Golshtein E. G., “Metod resheniya variatsionnykh neravenstv, opredelyaemykh monotonnymi otobrazheniyami”, Zh. vychisl. matem. i matem. fiz., 42:7 (2002), 958–968 | MR

[6] Ber K., Golshtein E. G., Sokolov N. A., “Ob ispolzovanii metoda urovnei dlya minimizatsii vypuklykh funktsii, ne vse znacheniya kotorykh konechny”, Ekonomika i matem. metody, 36:4 (2000), 95–107