Geodesic
A regularized extragradient method for solving equilibrium programming problems with an inexactly specified set
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 45 (2005) no. 4, pp. 650-660 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Unstable equilibrium problems are examined in which the objective function and the set where the equilibrium point is sought are inexactly specified. A regularized gradient-type method is proposed for solving such problems, and its convergence is analyzed. A regularizing operator is constructed. 
@article{ZVMMF_2005_45_4_a7,
     author = {A. S. Antipin and F. P. Vasil'ev and S. V. Shpirko},
     title = {A regularized extragradient method for solving equilibrium programming problems with an inexactly specified set},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {650--660},
     year = {2005},
     volume = {45},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2005_45_4_a7/}
}
TY  - JOUR
AU  - A. S. Antipin
AU  - F. P. Vasil'ev
AU  - S. V. Shpirko
TI  - A regularized extragradient method for solving equilibrium programming problems with an inexactly specified set
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2005
SP  - 650
EP  - 660
VL  - 45
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2005_45_4_a7/
LA  - ru
ID  - ZVMMF_2005_45_4_a7
ER  - 
%0 Journal Article
%A A. S. Antipin
%A F. P. Vasil'ev
%A S. V. Shpirko
%T A regularized extragradient method for solving equilibrium programming problems with an inexactly specified set
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2005
%P 650-660
%V 45
%N 4
%U http://geodesic.mathdoc.fr/item/ZVMMF_2005_45_4_a7/
%G ru
%F ZVMMF_2005_45_4_a7
A. S. Antipin; F. P. Vasil'ev; S. V. Shpirko. A regularized extragradient method for solving equilibrium programming problems with an inexactly specified set. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 45 (2005) no. 4, pp. 650-660. http://geodesic.mathdoc.fr/item/ZVMMF_2005_45_4_a7/

[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] Antipin A. S., “Ravnovesnoe programmirovanie: proksimalnye metody”, Avtomatika i telemekhan., 1997, no. 8, 125–137 | MR | Zbl

[4] Antipin A. S., “Rasscheplenie gradientnogo podkhoda dlya resheniya ekstremalnykh vklyuchenii”, Zh. vychisl. matem. i matem. fiz., 38:7 (1998), 1118–1132 | MR | Zbl

[5] Antipin A. S., Gradientnyi i ekstragradientnyi podkhody v bilineinom ravnovesnom programmirovanii, Preprint, VTs RAN, M., 2002, 130 pp.

[6] Tikhonov A. N., Arsenin V. Ya., Metody resheniya nekorrektnykh zadach, Nauka, M., 1986 | MR | Zbl

[7] Tikhonov A. N., Leonov A. S., Yagola A. G., Nelineinye nekorrektnye zadachi, Nauka. Fizmatlit, M., 1995 | MR

[8] Bakushinskii A. B., Goncharskii A. V., Iterativnye metody resheniya nekorrektnykh zadach, Nauka, M., 1989 | MR

[9] Vasilev F. P., Metody optimizatsii, Faktorial, M., 2002

[10] Antipin A. S., Vasilev F. P., “Metody regulyarizatsii dlya resheniya zadachi ravnovesnogo programmirovaniya s netochnymi vkhodnymi dannymi, osnovannye na rasshirenii mnozhestva”, Zh. vychisl. matem. i matem. fiz., 42:8 (2002), 1158–1165 | MR | Zbl

[11] Vasilev F. P., Antipin A. C., “Metody regulyarizatsii poiska nepodvizhnoi tochki ekstremalnykh otobrazhenii”, Vestn. MGU. Ser. 15. Vychisl. matem. i matem. fiz., 38:1 (1998), 11–14 | MR

[12] Antipin A. S., Vasilev F. P., “Metod stabilizatsii dlya resheniya zadach ravnovesnogo programmirovaniya”, Zh. vychisl. matem. i matem. fiz., 39:11 (1999), 1779–1786 | MR | Zbl

[13] Antipin A. S., Vasilev F. P., “Metod nevyazki dlya resheniya ravnovesnykh zadach s netochno zadannym mnozhestvom”, Zh. vychisl. matem. i matem. fiz., 41:1 (2001), 3–8 | MR | Zbl

[14] Antipin A. S., Vasilev F. P., Shpirko C. B., “Regulyarizovannyi ekstragradientnyi metod resheniya zadach ravnovesnogo programmirovaniya”, Zh. vychisl. matem. i matem. fiz., 43:10 (2003), 1451–1458 | MR | Zbl

[15] Korpelevich G. M., “Ekstragradientnyi metod dlya otyskaniya sedlovykh tochek i drugikh zadach”, Ekonomika i matem. metody, 12:4 (1976), 747–756 | MR | Zbl

[16] Shpirko C. B., Metod kososimmetrichnoi regulyarizatsii dlya resheniya zadach ravnovesnogo programmirovaniya, Dis. ...kand. fiz.-matem. nauk, VTs RAN, M., 2001

[17] Shpirko C. B., “O suschestvovanii i edinstvennosti resheniya zadachi ravnovesnogo programmirovaniya”, Izv. vuzov. Matematika, 2002, no. 12 (487), 79–83 | MR