Denisov S.V., Semenov V.V., Stetsyuk P.I.
Bregman extragradient method with monotone rule of step size tuning

A new extragradient-type method is proposed for approximate solution of variational inequalities with pseudo-monotone and Lipschitz-continuous operators acting in a finite-dimensional linear normed space. The method uses Bregman divergence (distance) instead of Euclidean distance and a new adjustment of step size, which does not require knowledge of the Lipschitz constant of the operator. In contrast to the previously used rules for choosing the step size, the method proposed in the paper does not perform additional calculations for the operator values and prox-map. A theorem on the convergence of the method is proved. © 2019, Springer Science+Business Media, LLC, part of Springer Nature.

Keywords: Bregman divergence, convergence, extragradient method, Lipschitz condition, pseudo-monotonicity, variational inequality, Computer science, Cybernetics, Bregman divergences, convergence, Extragradient methods, Lipschitz conditions, Monotonicity, Variational inequalities, Variational techniques

Cite:
Denisov S.V., Semenov V.V., Stetsyuk P.I. (2019). Bregman extragradient method with monotone rule of step size tuning. Cybernetics and Systems Analysis, 55 (3), 37-44. doi: https://doi.org/10.1007/s10559-019-00144-5 http://jnas.nbuv.gov.ua/article/UJRN-0000986315 [In Russian].