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<p/> <p>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 <inline-formula> <graphic file="1029-242X-2010-657192-i1.gif"/></inline-formula>-solution. Some preliminary computational results are reported.</p>