Preprint D109/2013
A direct splitting method for nonsmooth variational inequalities
J. Y. Bello Cruz | R. Díaz Millán
Keywords: Monotone variational inequalities | Maximal monotone operators | Splitting method | Projection methods.

In this paper, we propose a direct splitting method for solving
nonsmooth variational inequality problems in Hilbert spaces. The
weak convergence is established, when the operator is the sum of
two point-to-set and monotone operators. The proposed method is a
natural extension of the incremental subgradient method for
nondifferentiable optimization, which explores strongly the
structure of the operator using projected subgradient-like
techniques. The advantage of our method is that any nontrivial
subproblem must be solved, like the evaluation of the resolvent
operator. The necessity to compute proximal iterations is the main
difficult of others schemes for solving this kind of problem.