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

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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. 
@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/}
}
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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/