Abstract
We propose a modified extragradient method with dynamic step size adjustment to solve variational inequalities with monotone operators acting in a Hilbert space. In addition, we consider a version of the method that finds a solution of a variational inequality that is also a fixed point of a quasi-nonexpansive operator. We establish the weak convergence of the methods without any Lipschitzian continuity assumption on operators.
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Translated from Kibernetika i Sistemnyi Analiz, No. 5, September–October, 2015, pp. 102–110.
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Denisov, S.V., Semenov, V.V. & Chabak, L.M. Convergence of the Modified Extragradient Method for Variational Inequalities with Non-Lipschitz Operators. Cybern Syst Anal 51, 757–765 (2015). https://doi.org/10.1007/s10559-015-9768-z
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DOI: https://doi.org/10.1007/s10559-015-9768-z