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arXiv · 1605.07246

Adaptive ADMM with Spectral Penalty Parameter Selection

Zheng Xu·Mario A. T. Figueiredo·Tom Goldstein
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Abstract

The alternating direction method of multipliers (ADMM) is a versatile tool for solving a wide range of constrained optimization problems, with differentiable or non-differentiable objective functions. Unfortunately, its performance is highly sensitive to a penalty parameter, which makes ADMM often unreliable and hard to automate for a non-expert user. We tackle this weakness of ADMM by proposing a method to adaptively tune the penalty parameters to achieve fast convergence. The resulting adaptive ADMM (AADMM) algorithm, inspired by the successful Barzilai-Borwein spectral method for gradient descent, yields fast convergence and relative insensitivity to the initial stepsize and problem scaling.

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Zheng Xu, Mario A. T. Figueiredo, Tom Goldstein. 2016-05-24. Adaptive ADMM with Spectral Penalty Parameter Selection. https://arxiv.org/abs/1605.07246

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