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Optimal scaling of the ADMM algorithm for distributed quadratic programming

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

Abstract: This paper presents optimal scaling of the alternating directions method of multipliers (ADMM) algorithm for a class of distributed quadratic programming problems. The scaling corresponds to the ADMM step-size and relaxation parameter, as well as the edge-weights of the underlying communication graph. We optimize these parameters to yield the smallest convergence factor of the algorithm. Explicit expressions are derived for the step-size and relaxation parameter, as well as for the corresponding convergence factor. Numerical simulations justify our results and highlight the benefits of optimally scaling the ADMM algorithm.

Keywords: Alternating Direction Method of Multipliers, Optimal convergence factor

Category 1: Network Optimization

Category 2: Nonlinear Optimization (Quadratic Programming )

Citation: Submitted to the IEEE Transactions on Signal Processing. Prior work was presented at the 52nd IEEE Conference on Decision and Control, 2013.

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Entry Submitted: 03/26/2013
Entry Accepted: 04/01/2013
Entry Last Modified: 12/11/2014

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