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A quasi-Newton proximal splitting method
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- info:eu-repo/semantics/preprint
- Preprints, Working Papers, ...
- monotone operator
- proximal splitting
- scaled norm
- quasi-Newton
- 90C53, 90C06, 90C25, 90C30, 62J07, 47H05
- [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]
- [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA]
- [INFO]Computer Science [cs]