Geodesic
A two-step extragradient method for variational inequalities
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 9 (2010), pp. 82-85.

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

In this paper we consider an extragradient method for solving variational inequalities and related problems. On each iteration this method makes two trial steps along the gradient, and the value of the gradient at the second point is used at the first point as the iteration direction. We prove the convergence of this method in a general case. For problems with a bilinear functional we prove the geometric convergence rate.
Keywords: optimization, extragradiend method, variational inequality, saddle point. 
@article{IVM_2010_9_a7,
     author = {A. V. Zykina and N. V. Melenchuk},
     title = {A two-step extragradient method for variational inequalities},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {82--85},
     publisher = {mathdoc},
     number = {9},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2010_9_a7/}
}
TY  - JOUR
AU  - A. V. Zykina
AU  - N. V. Melenchuk
TI  - A two-step extragradient method for variational inequalities
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2010
SP  - 82
EP  - 85
IS  - 9
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2010_9_a7/
LA  - ru
ID  - IVM_2010_9_a7
ER  - 
%0 Journal Article
%A A. V. Zykina
%A N. V. Melenchuk
%T A two-step extragradient method for variational inequalities
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2010
%P 82-85
%N 9
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2010_9_a7/
%G ru
%F IVM_2010_9_a7
A. V. Zykina; N. V. Melenchuk. A two-step extragradient method for variational inequalities. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 9 (2010), pp. 82-85. http://geodesic.mathdoc.fr/item/IVM_2010_9_a7/

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

[2] Konnov I. V., “Kombinirovannye relaksatsionnye metody dlya poiska tochek ravnovesiya i resheniya smezhnykh zadach”, Izv. vuzov. Matematika, 1993, no. 2, 46–53 | MR | Zbl

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

[4] Zykina A. V., “Obratnaya dopolnitelnost v modeli upravleniya resursami”, Zhurn. vychisl. matem. i matem. fiz., 48:11 (2008), 1968–1978 | MR