Goldstein, TomO’Donoghue, BrendanSetzer, SimonBaraniuk, Richard2017-06-012017-06-012014Goldstein, Tom, O’Donoghue, Brendan, Setzer, Simon, et al.. "Fast Alternating Direction Optimization Methods." <i>SIAM Journal on Imaging Sciences,</i> 7, no. 3 (2014) Society for Industrial and Applied Mathematics: 1588-1623. http://dx.doi.org/10.1137/120896219.https://hdl.handle.net/1911/94752Alternating direction methods are a common tool for general mathematical programming and optimization. These methods have become particularly important in the field of variational image processing, which frequently requires the minimization of nondifferentiable objectives. This paper considers accelerated (i.e., fast) variants of two common alternating direction methods: the alternating direction method of multipliers (ADMM) and the alternating minimization algorithm (AMA). The proposed acceleration is of the form first proposed by Nesterov for gradient descent methods. In the case that the objective function is strongly convex, global convergence bounds are provided for both classical and accelerated variants of the methods. Numerical examples are presented to demonstrate the superior performance of the fast methods for a wide variety of problems.engArticle is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.Journal articleADMMsplittingoptimizationBregmanacceleratedNesterovmethod of multipliershttp://dx.doi.org/10.1137/120896219