A quasi-Newton proximal splitting method
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.