We introduce a relaxed-projection splitting algorithm for solving variationalinequalities in Hilbert spaces for the sum of nonsmooth maximal monotoneoperators, where the feasible set is defined by a nonlinear and nonsmoothcontinuous convex function inequality. In our scheme, the orthogonalprojections onto the feasible set are replaced by projections onto separatinghyperplanes. Furthermore, each iteration of the proposed method consists ofsimple subgradient-like steps, which does not demand the solution of anontrivial subproblem, using only individual operators, which exploits thestructure of the problem. Assuming monotonicity of the individual operators andthe existence of solutions, we prove that the generated sequence convergesweakly to a solution.
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