UDC 517.988
3 V.M. Glushkov Institute of Cybernetics of the National Academy of Sciences of Ukraine, Kyiv, Ukraine
 stetsyukp@gmail.com
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BREGMAN EXTRAGRADIENT METHOD WITH MONOTONE
RULE OF STEP SIZE TUNING
Abstract. A new extragradient-type method for the approximate solution of variational inequalities with pseudo-monotone and Lipschitz-continuous operators acting in a finite-dimensional linear normed space is proposed. The method uses the Bregman divergence (distance) instead of the Euclidean distance and the new adjustment of the step size which does not require knowledge of the Lipschitz constant of operator. In contrast to the previously used rules for choosing the step size, the proposed method does not perform additional calculations for the operator values and prox-map. A theorem on the convergence of the method is proved.
Keywords: variational inequality, pseudo-monotonicity, Lipschitz condition, extragradient method, Bregman divergence, convergence.
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