A discrete-time distributed algorithm for minimum l1-norm solution of an under-determined linear equation set

Xuan Wang*, Shaoshuai Mou*, Brian D.O. Anderson

*Corresponding author for this work

    Research output: Contribution to journalConference articlepeer-review

    1 Citation (Scopus)

    Abstract

    This paper proposes a discrete-time, distributed algorithm for multi-agent networks to achieve the minimum l1-norm solution to a group of linear equations known to possess a family of solutions. We assume each agent in the network knows only one equation and can communicate with only its neighbors. The algorithm is developed based on a combination of the projection-consensus idea and the sub-gradient descent method. Given the underlying network graph to be directed and strongly connected, we prove that the algorithm enables all agents to achieve a common minimum l1-norm solution. The major difficulty to be dealt with is the non-smooth nature of the norm and the lack of strict convexity of the associated relevant performance index.

    Original languageEnglish
    Pages (from-to)3278-3285
    Number of pages8
    JournalIFAC-PapersOnLine
    Volume53
    Issue number2
    DOIs
    Publication statusPublished - 2020
    Event21st IFAC World Congress 2020 - Berlin, Germany
    Duration: 12 Jul 202017 Jul 2020

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