Optimal scaling of the ADMM algorithm for distributed quadratic programming
André Teixeira (andreteikth.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.
Entry Submitted: 03/26/2013
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