Distributed optimisation design for solving the Stein equation with constraints
- Author(s): Guanpu Chen 1, 2 ; Xianlin Zeng 3 ; Yiguang Hong 1, 2
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View affiliations
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Affiliations:
1:
School of Mathematical Sciences , University of Chinese Academy of Sciences , 100049, Beijing , People's Republic of China ;
2: Key Laboratory of Systems and Control, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, 100190, Beijing , People's Republic of China ;
3: Key Laboratory of Intelligent Control and Decision of Complex Systems, School of Automation , Beijing Institute of Technology , 100081, Beijing , People's Republic of China
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Affiliations:
1:
School of Mathematical Sciences , University of Chinese Academy of Sciences , 100049, Beijing , People's Republic of China ;
- 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
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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