  In this paper we present a variant of the proximal forward-backward splitting
iteration for solving nonsmooth optimization problems in Hilbert spaces, when
the objective function is the sum of two nondifferentiable convex functions.
The proposed iteration, which will be called Proximal Subgradient Splitting
Method, extends the classical subgradient iteration for important classes of
problems, exploiting the additive structure of the objective function. The weak
convergence of the generated sequence was established using different stepsizes
and under suitable assumptions. Moreover, we analyze the complexity of the
iterates.
