caa a22 4500 605519145 CHVBK 20210128100729.0 cr unu---uuuuu 210128e20150901xx s 000 0 eng 10.1007/s10559-015-9768-z doi (NATIONALLICENCE)springer-10.1007/s10559-015-9768-z Convergence of the Modified Extragradient Method for Variational Inequalities with Non-Lipschitz Operators [Elektronische Daten] [S. Denisov, V. Semenov, L. Chabak] 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. Springer Science+Business Media New York, 2015 variational inequality nationallicence monotone operator nationallicence Hilbert space nationallicence extragradient method nationallicence weak convergence nationallicence Denisov S. Taras Shevchenko National University of Kyiv, Kyiv, Ukraine aut Semenov V. Taras Shevchenko National University of Kyiv, Kyiv, Ukraine aut Chabak L. Hetman Konashevych-Sahaidachnyi Kyiv State Maritime Academy, Kyiv, Ukraine aut Cybernetics and Systems Analysis Springer US; http://www.springer-ny.com 51/5(2015-09-01), 757-765 1060-0396 51:5<757 2015 51 10559 https://doi.org/10.1007/s10559-015-9768-z text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10559-015-9768-z text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Denisov S. Taras Shevchenko National University of Kyiv, Kyiv, Ukraine aut NATIONALLICENCE 700 1- Semenov V. Taras Shevchenko National University of Kyiv, Kyiv, Ukraine aut NATIONALLICENCE 700 1- Chabak L. Hetman Konashevych-Sahaidachnyi Kyiv State Maritime Academy, Kyiv, Ukraine aut NATIONALLICENCE 773 0- Cybernetics and Systems Analysis Springer US; http://www.springer-ny.com 51/5(2015-09-01), 757-765 1060-0396 51:5<757 2015 51 10559