Efficient evaluation of scaled proximal operators
arXiv:1603.05719
Abstract
Quadratic-support functions [Aravkin, Burke, and Pillonetto; J. Mach. Learn. Res. 14(1), 2013] constitute a parametric family of convex functions that includes a range of useful regularization terms found in applications of convex optimization. We show how an interior method can be used to efficiently compute the proximal operator of a quadratic-support function under different metrics. When the metric and the function have the right structure, the proximal map can be computed with cost nearly linear in the input size. We describe how to use this approach to implement quasi-Newton methods for a rich class of nonsmooth problems that arise, for example, in sparse optimization, image denoising, and sparse logistic regression.
23 pages
References in corpus (1)
Cited by in corpus (5)
- On Plug-and-Play Regularization using Linear Denoisers
- Generalized Self-Concordant Functions: A Recipe for Newton-Type Methods
- Optimization of Graph Total Variation via Active-Set-based Combinatorial Reconditioning
- Combinatorial Preconditioners for Proximal Algorithms on Graphs
- Further properties of the forward-backward envelope with applications to difference-of-convex programming