Journal of Inequalities and Applications
Volume 2010 (2010), Article ID 657192, 20 pages
Research Article

A New Method for Solving Monotone Generalized Variational Inequalities

Department of Mathematics, Kyungnam University, Masan, Kyungnam 631-701, Republic of Korea

Received 11 May 2010; Revised 27 August 2010; Accepted 4 October 2010

Academic Editor: Siegfried Carl

Copyright © 2010 Pham Ngoc Anh and Jong Kyu Kim. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We suggest new dual algorithms and iterative methods for solving monotone generalized variational inequalities. Instead of working on the primal space, this method performs a dual step on the dual space by using the dual gap function. Under the suitable conditions, we prove the convergence of the proposed algorithms and estimate their complexity to reach an 𝜖 -solution. Some preliminary computational results are reported.