A new modified extragradient method with Bregman divergence

1Semenov, VV
1Taras Shevchenko National University of Kyiv
Dopov. Nac. akad. nauk Ukr. 2018, 8:18-24
Section: Information Science and Cybernetics
Language: Russian
Abstract: 

A new method of the extragradient type for the approximate solution of variational inequalities with pseu-domonotone 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 the Bregman divergence instead of the Euclidean distance. A theorem on the convergence of the method is proved, and, in the case of a monotone operator, non-asymptotic estimates of the effectiveness of the method are obtained.

Keywords: Bregman divergence, convergence, extragradient method, Lipschitz condition, monotonicity, pseudomonotonicity, variational inequality
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