Geodesic
A regularized Newton method for solving equilibrium programming problems with an inexactly specified set
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 47 (2007) no. 1, pp. 21-33 
A. S. Antipin; F. P. Vasil'ev; A. S. Stukalov. A regularized Newton method for solving equilibrium programming problems with an inexactly specified set. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 47 (2007) no. 1, pp. 21-33. http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_1_a3/
@article{ZVMMF_2007_47_1_a3,
     author = {A. S. Antipin and F. P. Vasil'ev and A. S. Stukalov},
     title = {A~regularized {Newton} 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 = {21--33},
     year = {2007},
     volume = {47},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_1_a3/}
}
TY  - JOUR
AU  - A. S. Antipin
AU  - F. P. Vasil'ev
AU  - A. S. Stukalov
TI  - A regularized Newton method for solving equilibrium programming problems with an inexactly specified set
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2007
SP  - 21
EP  - 33
VL  - 47
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_1_a3/
LA  - ru
ID  - ZVMMF_2007_47_1_a3
ER  - 
%0 Journal Article
%A A. S. Antipin
%A F. P. Vasil'ev
%A A. S. Stukalov
%T A regularized Newton method for solving equilibrium programming problems with an inexactly specified set
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2007
%P 21-33
%V 47
%N 1
%U http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_1_a3/
%G ru
%F ZVMMF_2007_47_1_a3

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

Unstable equilibrium problems are examined in which the objective function and the set where the equilibrium point is sought are specified inexactly. A regularized Newton method, combined with penalty functions, is proposed for solving such problems, and its convergence is analyzed. A regularizing operator is constructed.

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

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

[5] Antipin A. C., Gradientnyi i ekstragradientnyi podkhody v bilineinom ravnovesnom programmirovanii, VTs RAN, M., 2002

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

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

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

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

[10] Vasilev F. P., Antipin A. C., “Metody regulyarizatsii poiska nepodvizhnoi tochki ekstremalnykh otobrazhenii”, Vestn. MGU. Ser. 15. Vychisl. matem. i kibernetika, 1998, no. 1, 11–14 | MR

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

[12] Antipin A. C., 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

[13] Antipin A. C., Vasilev F. P., “Metod kvazireshenii dlya resheniya zadachi ravnovesnogo programmirovaniya s netochno zadannym mnozhestvom mnozhestva”, Vestn. RUDN. Ser. Matematika, 8:2 (2002), 10–16

[14] Antipin A. C., 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

[15] Antipin A. C., 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

[16] Antipin A. C., Vasilev F. P., Shpirko C. B., “Regulyarizovannyi ekstragradientnyi metod resheniya zadach ravnovesnogo programmirovaniya s netochno zadannym mnozhestvom”, Zh. vychisl. matem. i matem. fiz., 45:4 (2005), 650–660 | MR | Zbl

[17] Antipin A. C., “Metod Nyutona dlya resheniya ravnovesnykh i igrovykh zadach”, Sb. statei “Nelineinaya dinamika i upravlenie”, v. 3, Fizmatlit, M., 2003, 123–138

[18] Baiokki K., Kapelo A., Variatsionnye i kvazivariatsionnye neravenstva. Prilozhenie k zadacham so svobodnoi granitsei, Nauka, M., 1988 | MR