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Accelerated Block-Coordinate Relaxation for Regularized Optimization

Stephen Wright (swright***at***cs.wisc.edu)

Abstract: We discuss minimization of a smooth function to which is added a separable regularization function that induces structure in the solution. A block-coordinate relaxation approach with proximal linearized subproblems yields convergence to critical points, while identification of the optimal manifold (under a nondegeneracy condition) allows acceleration techniques to be applied on a reduced space. The work is motivated by experience with an algorithm for regularized logistic regression, and computational results for the algorithm on problems of this type are presented.

Keywords: regularized optimization, block coordinate relaxation, active manifold identification

Category 1: Convex and Nonsmooth Optimization (Nonsmooth Optimization )

Category 2: Applications -- Science and Engineering (Statistics )

Citation: SIAM Journal on Optimization 22 (2012), pp. 159-186. PDF available here http://pages.cs.wisc.edu/~swright/papers/80856.pdf

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Entry Submitted: 08/10/2010
Entry Accepted: 08/10/2010
Entry Last Modified: 04/16/2012

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