Copyright © 2010 Yonghong Yao et al. This is an open access article distributed under the
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We consider the following hierarchical equilibrium problem and variational inequality problem (abbreviated as HEVP): find a point such that , for all , where ,
are two monotone operators and is the solution of the equilibrium problem of finding such that , for all . We note that the problem (HEVP) includes some problems, for example, mathematical program and hierarchical minimization problems as special cases. For solving (HEVP), we propose a double-net algorithm which generates a net . We prove that the net hierarchically converges to the solution of (HEVP); that is, for each fixed , the net converges in norm, as , to a solution of the equilibrium problem, and as , the net converges in norm to the unique solution of (HEVP).