  We introduce a relaxed-projection splitting algorithm for solving variational
inequalities in Hilbert spaces for the sum of nonsmooth maximal monotone
operators, where the feasible set is defined by a nonlinear and nonsmooth
continuous convex function inequality. In our scheme, the orthogonal
projections onto the feasible set are replaced by projections onto separating
hyperplanes. Furthermore, each iteration of the proposed method consists of
simple subgradient-like steps, which does not demand the solution of a
nontrivial subproblem, using only individual operators, which exploits the
structure of the problem. Assuming monotonicity of the individual operators and
the existence of solutions, we prove that the generated sequence converges
weakly to a solution.
