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A quasi-Newton proximal splitting method

Stephen Becker(stephen.beckr***at***gmail.com)
Jalal Fadili(Jalal.Fadili***at***greyc.ensicaen.fr)

Abstract: A new result in convex analysis on the calculation of proximity operators in certain scaled norms is derived. We describe efficient implementations of the proximity calculation for a useful class of functions; the implementations exploit the piece-wise linear nature of the dual problem. The second part of the paper applies the previous result to acceleration of convex minimization problems, and leads to an elegant quasi-Newton method. The optimization method compares favorably against state-of-the-art alternatives. The algorithm has extensive applications including signal processing, sparse recovery and machine learning and classification.

Keywords: quasi-Newton; proximal algorithm; proximity operator; scaled norms

Category 1: Convex and Nonsmooth Optimization (Convex Optimization )

Category 2: Nonlinear Optimization (Constrained Nonlinear Optimization )

Category 3: Convex and Nonsmooth Optimization (Nonsmooth Optimization )

Citation: also at http://arxiv.org/abs/1206.1156

Download: [PDF]

Entry Submitted: 06/20/2012
Entry Accepted: 06/20/2012
Entry Last Modified: 06/20/2012

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