Alternating Linearization for Structured Regularization Problems

Details Alternating Linearization for Structured Regularization Problems Alternating Linearization for Structured Regularization Problems

Publishing date

2011-12-31

URL

arxiv.org/abs/1201.0306v1

Science

Statistics

Field

Computation

Type

Scientific paper

Abstract

We adapt the alternating linearization method for proximal decomposition to structured regularization problems, in particular, to the generalized lasso problems. The method is related to two well-known operator splitting methods, the Douglas-Rachford and the Peaceman-Rachford method, but it has descent properties with respect to the objective function. Its convergence mechanism is related to that of bundle methods of nonsmooth optimization. We also discuss implementation for very large problems, with the use of specialized algorithms and sparse data structures. Finally, we present numerical results for several synthetic and real-world examples, including a three-dimensional fused lasso problem, which illustrate the scalability, efficacy, and accuracy of the method.

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