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Alternating Proximal Gradient Method for Convex Minimization

Shiqian Ma (sm2756***at***gmail.com)

Abstract: In this paper, we propose an alternating proximal gradient method that solves convex minimization problems with three or more separable blocks in the objective function. Our method is based on the framework of alternating direction method of multipliers. The main computational effort in each iteration of the proposed method is to compute the proximal mappings of the involved convex functions. The global convergence result of the proposed method is established. We show that many interesting problems arising from machine learning, statistics, medical imaging and computer vision can be solved by the proposed method. Numerical results on problems such as latent variable graphical model selection, stable principal component pursuit and compressive principal component pursuit are presented.

Keywords: Alternating Direction Method of Multipliers, Proximal Gradient Method, Global Convergence, Sparse and Low-Rank Optimization

Category 1: Convex and Nonsmooth Optimization (Convex Optimization )


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Entry Submitted: 09/15/2012
Entry Accepted: 09/15/2012
Entry Last Modified: 09/15/2012

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