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Journal of Automation and Information Sciences
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ISSN Druckformat: 1064-2315
ISSN Online: 2163-9337

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Journal of Automation and Information Sciences

DOI: 10.1615/JAutomatInfScien.v50.i8.30
pages 26-37

Modified Extragradient Method with Bregman Divergence for Variational Inequalities

Vladimir V. Semenov
Kiev National Taras Shevchenko University, Kiev


A new method of extragradient type for the approximate solution of variational inequalities with pseudomonotone and Lipschitz-continuous operators acting in a finite-dimensional linear normed space is proposed. This method is a modification of the subgradient extragradient algorithm using Bregman divergence instead of Euclidean distance. Like other schemes using Bregman divergence the proposed method can sometimes effectively take into account a structure of a feasible set of the problem. The theorem on the method convergence is proved and in the case of a monotone operator nonasymptotic estimates of the method effectiveness are obtained


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