Copyright © 2011 Yonghong Yao and Yeong Cheng Liou. 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.
As a well-known numerical method, the extragradient method solves numerically
the variational inequality of finding
such that , for all . In this paper, we devote to solve the following hierarchical variational inequality
Find such that , for all . We first suggest and analyze an implicit extragradient method for solving the hierarchical
variational inequality . It is shown that the net defined by the
suggested implicit extragradient method converges strongly to the unique solution
of in Hilbert spaces. As a special case, we obtain the minimum norm
solution of the variational inequality .