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In this paper we present a variant of the proximal forward-backward splittingiteration for solving nonsmooth optimization problems in Hilbert spaces, whenthe objective function is the sum of two nondifferentiable convex functions.The proposed iteration, which will be called Proximal Subgradient SplittingMethod, extends the classical subgradient iteration for important classes ofproblems, exploiting the additive structure of the objective function. The weakconvergence of the generated sequence was established using different stepsizesand under suitable assumptions. Moreover, we analyze the complexity of theiterates.

On proximal subgradient splitting method for minimizing the sum of two nonsmooth convex functions