Finite number of iterations in the two-step extragradient method
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 9 (2014), pp. 75-79.

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

We consider two-step extragradient method. This method is used for solving variational inequalities and related problems. We show the convergence of the method in a finite number of iterations when the condition of sharpness is fulfilled.
Keywords: optimization, extragradient method, variational inequality, condition of sharpness.
@article{IVM_2014_9_a7,
     author = {A. V. Zykina and N. V. Melen'chuk},
     title = {Finite number of iterations in the two-step extragradient method},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {75--79},
     publisher = {mathdoc},
     number = {9},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2014_9_a7/}
}
TY  - JOUR
AU  - A. V. Zykina
AU  - N. V. Melen'chuk
TI  - Finite number of iterations in the two-step extragradient method
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2014
SP  - 75
EP  - 79
IS  - 9
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2014_9_a7/
LA  - ru
ID  - IVM_2014_9_a7
ER  - 
%0 Journal Article
%A A. V. Zykina
%A N. V. Melen'chuk
%T Finite number of iterations in the two-step extragradient method
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2014
%P 75-79
%N 9
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2014_9_a7/
%G ru
%F IVM_2014_9_a7
A. V. Zykina; N. V. Melen'chuk. Finite number of iterations in the two-step extragradient method. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 9 (2014), pp. 75-79. http://geodesic.mathdoc.fr/item/IVM_2014_9_a7/

[1] Konnov I. V., Combined relaxation methods for variational inequalities, Springer-Verlag, Berlin, 2001 | MR | Zbl

[2] Antipin A. S., “Ekstraproksimalnyi metod resheniya ravnovesnykh i igrovykh zadach”, Zhurn. vychisl. matem. i matem. fiz., 45:11 (2005), 1969–1990 | MR | Zbl

[3] Antipin A. S., Artemeva L. A., Vasilev F. P., “Nepreryvnyi ekstragradientnyi metod resheniya parametricheskoi mnogokriterialnoi zadachi ravnovesnogo programmirovaniya”, Differents. uravneniya, 45:11 (2009), 1577–1585 | MR | Zbl

[4] Antipin A. S., “O metode vypuklogo programmirovaniya, ispolzuyuschem simmetricheskuyu modifikatsiyu funktsii Lagranzha”, Ekonomika i matem. metody, 12:6 (1976), 1164–1173 | Zbl

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

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

[7] Zykina A. V., Melenchuk N. V., “Dvukhshagovyi ekstragradientnyi metod dlya zadachi upravleniya resursami”, Modelirovanie i analiz informatsionnykh sistem, 17:1 (2010), 65–75

[8] Zykina A. V., Melenchuk N. V., “Dvukhshagovyi ekstragradientnyi metod dlya variatsionnykh neravenstv”, Izv. vuzov. Matem., 2010, no. 9, 82–85 | MR | Zbl

[9] Vasilev F. P., Nedich A., “O trekhshagovom regulyarizovannom metode proektsii gradienta dlya resheniya zadach minimizatsii s netochnymi iskhodnymi dannymi”, Izv. vuzov. Matem., 1993, no. 12, 35–43 | MR | Zbl

[10] Antipin A. S., Nedich A., Yachimovich M., “Trekhshagovyi metod linearizatsii dlya zadach minimizatsii”, Izv. vuzov. Matem., 1994, no. 12, 3–7 | MR | Zbl

[11] Malinov V. G., “O regulyarizovannom dvukhshagovom proektsionnom metode dlya zadach minimizatsii s ogranicheniyami”, Zhurn. vychisl. matem. i matem. fiz., 40:1 (2000), 65–71 | MR | Zbl

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

[13] Polyak B. T., Vvedenie v optimizatsiyu, 2-e izd., LENARD, M., 2014

[14] Zaporozhets D. N., Zykina A. V., Melenchuk N. V., “Sravnitelnyi analiz ekstragradientnykh metodov resheniya variatsionnykh neravenstv dlya nekotorykh zadach”, Avtomatika i telemekhanika, 2012, no. 4, 32–46