Optimal scaling of the ADMM algorithm for distributed quadratic programming
Andr\'e Teixeira, Euhanna Ghadimi, Iman Shames, Henrik Sandberg,, Mikael Johansson
TL;DR
This paper derives optimal parameter settings for the ADMM algorithm to enhance convergence speed in distributed quadratic programming, providing explicit formulas and numerical validation.
Contribution
It introduces a method to optimally scale ADMM parameters, including step-size, relaxation, and edge-weights, for improved convergence in distributed quadratic problems.
Findings
Explicit formulas for optimal ADMM parameters
Reduced convergence factor with optimal scaling
Numerical simulations confirm theoretical improvements
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.
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