A quasi-Newton proximal splitting method

A new result in convex analysis on the calculation of proximity operators in certain scalednorms is derived. We describe efficient implementations of the proximity calculationfor 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 againststate-of-the-art alternatives. The algorithm has extensive applications including signal processing, sparse recovery and machine learning and classification.