Scalable, Distributed Algorithms for Solving Linear Equations via Double-Layered Networks

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

doi:10.1109/tac.2019.2919101

Cited by 32 publications

(20 citation statements)

References 40 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Recently, in [22], a continuous-time distributed algorithm with scalar state is proposed for solving linear equation, in which each agent has only access to two scalar elements of A and b, and the estimated states are also two scalars. Furthermore, some scalable distributed algorithms for solving linear equations are proposed by introducing double-layered multi-agent networks in [23]. However, the proposed algorithms in [22], [23] are only effective for the linear equations that have exact solutions, and cannot be applied for over-determined linear equations to achieve a least square solution.…”

Section: Introductionmentioning

confidence: 99%

“…Furthermore, some scalable distributed algorithms for solving linear equations are proposed by introducing double-layered multi-agent networks in [23]. However, the proposed algorithms in [22], [23] are only effective for the linear equations that have exact solutions, and cannot be applied for over-determined linear equations to achieve a least square solution.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Distributed algorithms for the least square solution of linear equations

Huang,

Meng

2021

Preprint

View full text Add to dashboard Cite

This paper proposes distributed algorithms for solving linear equations to seek a least square solution via multiagent networks. We consider that each agent has only access to a small and imcomplete block of linear equations rather than the complete row or column in the existing literatures. Firstly, we focus on the case of a homogeneous partition of linear equations. A distributed algorithm is proposed via a single-layered grid network, in which each agent only needs to control three scalar states. Secondly, we consider the case of heterogeneous partitions of linear equations. Two distributed algorithms with doubledlayered network are developed, which allows each agent's states to have different dimensions and can be applied to heterogeneous agents with different storage and computation capability. Rigorous proofs show that the proposed distributed algorithms collaboratively obtain a least square solution with exponential convergence, and also own a solvability verification property, i.e., a criterion to verify whether the obtained solution is an exact solution. Finally, some simulation examples are provided to demonstrate the effectiveness of the proposed algorithms.

show abstract

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Distributed algorithms for the least square solution of linear equations

Huang,

Meng

2021

Preprint

View full text Add to dashboard Cite

show abstract

“…One of the most interesting relevant problems is to solve algebraic equations in a distributed way, including linear equations and matrix equations. There have been several distributed algorithms for solving

A x = b

Section: Introductionmentioning

confidence: 99%

“…There have been several distributed algorithms for solving

A x = b

in a multi‐agent setting [5–10]. For different data partitions, every agent only holds a row sub‐block [5, 6], a column sub‐block [7] or specific sub‐block in a double‐layered network [8] of data matrix A . For different assumptions of solutions, there are diverse algorithms for a unique solution, a least‐squares solution [9] and a minimise weighted norm solution in the multiple solutions case [11].…”

Section: Introductionmentioning

confidence: 99%

Distributed optimisation approach to least‐squares solution of Sylvester equations

Deng

Zeng

2020

IET Control Theory & Appl

View full text Add to dashboard Cite

“…It is shown that, with a properly-designed stepsize that converges to zero fast enough, the states can be refined towards an optimal solution. Based on the subgradient method, some excellent distributed optimization algorithms are developed from varieties of perspectives, working on improving convergence accuracy, relaxing stepsize requirement, accelerating convergence rate and so on [19]- [23]. In [24], [25], a stochastic theory based projection method with Gaussian assumptions is also used to evaluate ambiguous local utilities instead of exact gradients.…”

Section: Introductionmentioning

confidence: 99%

Distributed Constrained Consensus of Utilities via a Self Evaluation Approach

Wang

Sun

2019

IEEE Access

View full text Add to dashboard Cite

This paper investigates the problem of distributed constrained consensus of utilities for multiple networked nodes, which is essentially challenging in view of the fact that local constraints may hinder the global optimization across the network. Focusing on this problem, a generalized framework is developed via a self evaluation approach, in which each node uses utility evaluations to update individual states by interacting with neighbors only. Following the framework, the distributed constrained consensus algorithms is derived, with theoretical analyses presented to show the convergence and stability. In addition, an approximation method is proposed as well for ease of engineering implementation. Finally, illustrative examples are provided and analyzed to substantiate the efficacy of the proposed algorithm.

show abstract

Scalable, Distributed Algorithms for Solving Linear Equations via Double-Layered Networks

Cited by 32 publications

References 40 publications

Distributed algorithms for the least square solution of linear equations

Distributed algorithms for the least square solution of linear equations

Distributed optimisation approach to least‐squares solution of Sylvester equations

Distributed Constrained Consensus of Utilities via a Self Evaluation Approach

Contact Info

Product

Resources

About