Geodesic
A first-order continuous method for the Antipin regularization of monotone variational inequalities in a Banach space
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 46 (2006) no. 7, pp. 1184-1194 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

The concept of a generalized projection operator onto a convex closed subset of a Banach space is modified. This operator is used to construct a first-order continuous method for the Antipin regularization of monotone variational inequalities in a Banach space. Sufficient conditions for the convergence of the method are found. 
@article{ZVMMF_2006_46_7_a2,
     author = {I. P. Ryazantseva},
     title = {A~first-order continuous method for the {Antipin} regularization of monotone variational inequalities in {a~Banach} space},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1184--1194},
     year = {2006},
     volume = {46},
     number = {7},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_7_a2/}
}
TY  - JOUR
AU  - I. P. Ryazantseva
TI  - A first-order continuous method for the Antipin regularization of monotone variational inequalities in a Banach space
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2006
SP  - 1184
EP  - 1194
VL  - 46
IS  - 7
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_7_a2/
LA  - ru
ID  - ZVMMF_2006_46_7_a2
ER  - 
%0 Journal Article
%A I. P. Ryazantseva
%T A first-order continuous method for the Antipin regularization of monotone variational inequalities in a Banach space
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2006
%P 1184-1194
%V 46
%N 7
%U http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_7_a2/
%G ru
%F ZVMMF_2006_46_7_a2
I. P. Ryazantseva. A first-order continuous method for the Antipin regularization of monotone variational inequalities in a Banach space. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 46 (2006) no. 7, pp. 1184-1194. http://geodesic.mathdoc.fr/item/ZVMMF_2006_46_7_a2/

[1] Antipin A. C., “Nepreryvnye i iterativnye protsessy s operatorami proektirovaniya i tipa proektirovaniya”, Vopr. kibernetiki. Vychisl. vopr. analiza bolshikh sistem, Nauchn. sovet po kompleksnoi probleme “Kibernetika” AN SSSR, M., 1989, 5–43 | MR

[2] Ryazantseva I. P., “Nepreryvnye i iterativnye metody pervogo poryadka s operatorom obobschennogo proektirovaniya dlya monotonnykh variatsionnykh neravenstv v banakhovom prostranstve”, Zh. vychisl. matem. i matem. fiz., 45:3 (2005), 400–410 | MR | Zbl

[3] Alber Ya. I., Metody resheniya nelineinykh operatornykh uravnenii i variatsionnykh neravenstv v banakhovykh prostranstvakh, Dis. $\dots$ dokt. fiz.-matem. nauk, NGU, Novosibirsk, 1986

[4] Alber Ya. I., “Generalized projection operators in Banach spaces: Properties and applications”, Funct. Different. Equat., 1:1 (1994), 1–21 | MR

[5] Nedich A., “Regulyarizovannyi nepreryvnyi metod proektsii gradienta dlya zadach minimizatsii s netochnymi iskhodnymi dannymi”, Vestn. MGU. Ser. 15, 1994, no. 1, 3–10 | MR | Zbl

[6] Vainberg M. M., Variatsionnyi metod i metod monotonnykh operatorov v teorii nelineinykh uravnenii, Nauka, M., 1972 | MR | Zbl

[7] Lions Zh. L., Nekotorye metody resheniya nelineinykh kraevykh zadach, Mir, M., 1972 | MR

[8] Yurgelas V. V., Metody priblizhennogo resheniya uravnenii s monotonnymi operatorami, Dis. $\dots$ kand. fiz.-matem. nauk, VGU, Voronezh, 1983

[9] Raevskii X., Greger K., Zakharias K., Nelineinye operatornye uravneniya i operatornye differentsialnye uravneniya, Mir, M., 1978 | MR

[10] Figiel T., “On the moduli of convexity and smoothness”, Studia Math., 56:2 (1976), 121–155 | MR | Zbl

[11] Distel D., Geometriya banakhovykh prostranstv, Vischa shkola, Kiev, 1980 | MR

[12] Notik A. I., Geometriya banakhovykh prostranstv i priblizhennye metody resheniya nelineinykh uravnenii i zadach optimizatsii, Dis. $\dots$ kand. fiz.-matem. nauk, VGU, Voronezh, 1986

[13] Vladimirov V. V., Nesterov Yu. E., Chekanov Yu. N., “O ravnomerno vypuklykh funktsionalakh”, Vestn. MGU. Ser. 15, 1972, no. 3, 12–23

[14] Kolmogorov A. N., Fomin C. B., Elementy teorii funktsii i funktsionalnogo analiza, Nauka, M., 1976 | MR

[15] Pascali D., Sburlan S., Nonlinear operators of monotone type, R.S.R., Bucureşti, 1978

[16] Vasilev F. P., Chislennye metody resheniya ekstremalnykh zadach, Nauka, M., 1988 | MR

[17] Ryazantseva I. P., Ustoichivye metody resheniya nelineinykh monotonnykh nekorrektnykh zadach, Dis. $\dots$ dokt. fiz.-matem. nauk, NGU, Novosibirsk, 1996

[18] Vasilev F. P., Metody resheniya ekstremalnykh zadach, Nauka, M., 1981 | MR

[19] Ryazantseva I. P., “Nepreryvnyi metod regulyarizatsii pervogo poryadka dlya monotonnykh variatsionnykh neravenstv v banakhovom prostranstve”, Differents. ur-niya, 39:1 (2003), 113–117 | MR | Zbl

[20] Ryazantseva I. P., Bubnova O. Yu., “Nepreryvnyi metod vtorogo poryadka dlya nelineinykh akkretivnykh uravnenii v banakhovom prostranstve”, Tr. Srednevolzhskogo matem. ob-va, 3–4:1 (2002), 327–334

[21] Alber Ya., Butnariu D., Ryazantseva I., “Regularization methods for ill-posed inclusions and variational inequalities with domain perturbations”, J. Nonlinear and Convex Analys., 2:1 (2001), 53–79 | MR | Zbl

[22] Ryazantseva I. P., “Ob odnom sposobe approksimatsii reshenii variatsionnykh neravenstv s monotonnymi operatorami v banakhovom prostranstve pri priblizhennom zadanii dannykh”, Differents. ur-niya, 40:8 (2004), 1108–1117 | MR | Zbl