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Izv. Vyssh. Uchebn. Zaved. Mat., 2010, Number 9, Pages 82–85 (Mi ivm7131)  

This article is cited in 4 scientific papers (total in 4 papers)

Brief communications

A two-step extragradient method for variational inequalities

A. V. Zykina, N. V. Melenchuk

Omsk State Technical University, Omsk, Russia

Abstract: 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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English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2010, 54:9, 71–73

Bibliographic databases:

Document Type: Article
UDC: 519.85
Received: 05.02.2010

Citation: A. V. Zykina, N. V. Melenchuk, “A two-step extragradient method for variational inequalities”, Izv. Vyssh. Uchebn. Zaved. Mat., 2010, no. 9, 82–85; Russian Math. (Iz. VUZ), 54:9 (2010), 71–73

Citation in format AMSBIB
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\by A.~V.~Zykina, N.~V.~Melenchuk
\paper A two-step extragradient method for variational inequalities
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2010
\issue 9
\pages 82--85
\mathnet{http://mi.mathnet.ru/ivm7131}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2789310}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2010
\vol 54
\issue 9
\pages 71--73
\crossref{https://doi.org/10.3103/S1066369X10090082}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-78649551794}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Zaporozhets D.N., Zykin V.S., Zykina A.V., Kuyanov D.I., “Rasparallelivanie ekstragradientnykh metodov”, Omskii nauchnyi vestnik, 2011, no. 103, 22–25  elib
    2. D. N. Zaporozhets, A. V. Zykina, N. V. Melen'chuk, “Comparative analysis of the extragradient methods for solution of the variational inequalities of some problems”, Autom. Remote Control, 73:4 (2012), 626–636  mathnet  crossref  isi
    3. Zaporozhets D.N., Zykina A.V., “Dvukhshagovyi ekstragradientnyi metod s pamyatyu dlya resheniya variatsionnykh neravenstv so svyazannymi ogranicheniyami”, Omskii nauchnyi vestnik, 2012, no. 113, 274–277  elib
    4. A. V. Zykina, N. V. Melen'chuk, “Finite number of iterations in the two-step extragradient method”, Russian Math. (Iz. VUZ), 58:9 (2014), 62–65  mathnet  crossref
  • Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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