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Optimal parameter selection for the alternating direction method of multipliers (ADMM): quadratic problems

Euhanna Ghadimi (euhanna***at***kth.se)
André Teixeira (andretei***at***kth.se)
Iman Shames (iman.shames***at***unimleb.edu.au)
Mikael Johansson (mikaelj***at***kth.se)

Abstract: The alternating direction method of multipliers (ADMM) has emerged as a powerful technique for large-scale structured optimization. Despite many recent results on the convergence properties of ADMM, a quantitative characterization of the impact of the algorithm parameters on the convergence times of the method is still lacking. In this paper we find the optimal algorithm parameters that minimize the convergence factor of the ADMM iterates in the context of $\ell_2$-regularized minimization and constrained quadratic programming. Numerical examples show that our parameter selection rules significantly outperform existing alternatives in the literature.

Keywords: ADMM, Convergence Rate, Convergence Factor

Category 1: Convex and Nonsmooth Optimization (Convex Optimization )

Category 2: Nonlinear Optimization (Quadratic Programming )

Citation: DOI 10.1109/TAC.2014.2354892, IEEE Transactions on Automatic Control

Download: [PDF]

Entry Submitted: 06/10/2013
Entry Accepted: 06/10/2013
Entry Last Modified: 12/11/2014

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