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

José Yunier Bello Cruz(yunier***at***impa.br)

Abstract: In this paper we present a variant of the proximal forward-backward splitting method 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 call the Proximal Subgradient Splitting Method, extends the classical projected 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.

Keywords: Convex problems; Nonsmooth optimization problems; Proximal forward-backward splitting iteration; Subgradient method.

Category 1: Convex and Nonsmooth Optimization

Category 2: Nonlinear Optimization

Category 3: Global Optimization


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Entry Submitted: 11/17/2014
Entry Accepted: 11/17/2014
Entry Last Modified: 11/17/2014

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