The ADMM algorithm for distributed quadratic problems: Parameter selection and constraint preconditioning

André Teixeira, Euhanna Ghadimi, Iman Shames, Henrik Sandberg, Mikael Johansson

Research output: Contribution to journalArticlepeer-review

28 Citations (Scopus)

Abstract

This paper presents optimal parameter selection and preconditioning of the alternating direction method of multipliers (ADMM) algorithm for a class of distributed quadratic problems, which can be formulated as equality-constrained quadratic programming problems. The parameter selection focuses on the ADMM step-size and relaxation parameter, while the preconditioning corresponds to selecting the edge weights of the underlying communication graph. We optimize these parameters to yield the smallest convergence factor of the iterates. 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 optimal parameter selection and preconditioning for the ADMM algorithm.

Original languageEnglish
Article number7271111
Pages (from-to)290-305
Number of pages16
JournalIEEE Transactions on Signal Processing
Volume64
Issue number2
DOIs
Publication statusPublished - 15 Jan 2016
Externally publishedYes

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