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access icon free Distributed optimisation design for solving the Stein equation with constraints

  • Author(s): Guanpu Chen 1, 2 ; Xianlin Zeng 3 ; Yiguang Hong 1, 2
    • View affiliations
  • Source: Volume 13, Issue 15, 15 October 2019, p. 2492 – 2499
    DOI:  10.1049/iet-cta.2019.0140 , Print ISSN 1751-8644, Online ISSN 1751-8652
© The Institution of Engineering and Technology
Received 30/01/2019, Accepted 01/07/2019, Revised 16/06/2019, Published 02/07/2019

In this study, the authors consider distributed computation of the Stein equations with set constraints, where each agent or node knows a few rows or columns of coefficient matrices. By formulating an equivalent distributed optimisation problem, they propose a projection-based algorithm to seek least-squares solutions to the constrained Stein equation over a multi-agent system network. Then, they rigorously prove the convergence of the proposed algorithm to a least-squares solution for any initial condition, and moreover, provide a simplified distributed algorithm with an exponential convergence rate for the case without constraints.

Inspec keywords: least squares approximations; convergence; gradient methods; matrix algebra; multi-agent systems; concave programming

Other keywords: least-squares solution; equivalent distributed optimisation problem; distributed optimisation design; coefficient matrices; constrained Stein equation; columns; projection-based algorithm; set constraints; simplified distributed algorithm; Stein equations; multiagent system network; rows

Subjects: Optimisation techniques; Other topics in statistics; Linear algebra (numerical analysis); Statistics; Optimisation techniques; Other topics in statistics; Linear algebra (numerical analysis); Optimisation; Numerical analysis

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