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

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