caa a22 4500 463170016 CHVBK 20180406164810.0 cr unu---uuuuu 170326e20070201xx s 000 0 eng 10.1007/s10957-006-9060-5 doi (NATIONALLICENCE)springer-10.1007/s10957-006-9060-5 Han D. School of Mathematics and Computer Science, Nanjing Normal University, Nanjing, China aut Inexact Operator Splitting Methods with Selfadaptive Strategy for Variational Inequality Problems [Elektronische Daten] [D. Han] The Peaceman-Rachford and Douglas-Rachford operator splitting methods are advantageous for solving variational inequality problems, since they attack the original problems via solving a sequence of systems of smooth equations, which are much easier to solve than the variational inequalities. However, solving the subproblems exactly may be prohibitively difficult or even impossible. In this paper, we propose an inexact operator splitting method, where the subproblems are solved approximately with some relative error tolerance. Another contribution is that we adjust the scalar parameter automatically at each iteration and the adjustment parameter can be a positive constant, which makes the methods more practical and efficient. We prove the convergence of the method and present some preliminary computational results, showing that the proposed method is promising. Springer Science+Business Media, Inc., 2007 Variational inequality problems nationallicence operator splitting methods nationallicence inexact methods nationallicence self-adaptive algorithms nationallicence strongly monotone mappings nationallicence Journal of Optimization Theory and Applications Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 132/2(2007-02-01), 227-243 0022-3239 132:2<227 2007 132 10957 https://doi.org/10.1007/s10957-006-9060-5 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10957-006-9060-5 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Han D. School of Mathematics and Computer Science, Nanjing Normal University, Nanjing, China aut NATIONALLICENCE 773 0- Journal of Optimization Theory and Applications Kluwer Academic Publishers-Plenum Publishers; http://www.springer-ny.com 132/2(2007-02-01), 227-243 0022-3239 132:2<227 2007 132 10957 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer