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Essentially Decentralized Conjugate Gradients

Alexander Engelmann,T. Faulwasser

Published 2021 in Unknown venue

ABSTRACT

Solving structured systems of linear equations in a non-centralized fashion is an important step in many distributed optimization and control algorithms. Fast convergence is required in manifold applications. Known decentralized algorithms, however, typically exhibit asymptotic convergence at a linear rate. This note proposes an essentially decentralized variant of the Conjugate Gradient algorithm (d-CG). The proposed method exhibits a practical superlinear convergence rate and comes with a priori computable finite-step convergence guarantees. In contrast to previous works, we consider sum-wise decomposition instead of row-wise decomposition which enables application in multi-agent settings. We illustrate the performance of d-CG on problems from sensor fusion and compare the results to the widely-used Alternating Direction Method of Multipliers.

PUBLICATION RECORD

  • Publication year

    2021

  • Venue

    Unknown venue

  • Publication date

    2021-02-24

  • Fields of study

    Mathematics, Computer Science, Engineering

  • Identifiers
    arXiv 2102.12311
  • External record

    Open on Semantic Scholar

  • Source metadata

    Semantic Scholar

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