Geodesic
A two-step extragradient method for variational inequalities
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 9 (2010), pp. 82-85 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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     title = {A two-step extragradient method for variational inequalities},
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}
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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