A Distributed Algorithm for Solving Linear Algebraic Equations Over Random Networks

Seyyed Shaho Alaviani1, Nicola Elia2

  • 1Iowa State University
  • 2University of Minnesota

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Regular Session

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10:00 - 12:00 | Mon 17 Dec | Glitter | MoA03

Agent-Based Systems I

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Abstract

In this paper, the problem of solving linear algebraic equations of the form $Ax=b$ among multi agents is considered. It is assumed that the interconnection graphs over which the agents communicate are random. It is assumed that each agent only knows a subset of rows of the partitioned matrix $[A,b]$. The problem is formulated such that this formulation does not require distribution dependency of random communication graphs. The random Krasnoselskii-Mann iterative algorithm is applied for almost sure convergence to a solution of the problem for any matrices $A$ and $b$ and any initial conditions of agents' states. The algorithm converges almost surely independently from the distribution and, therefore, is amenable to completely asynchronous operations withot B-connectivity assumption. Based on initial conditions of agents' states, we show that the limit point of the sequence generated by the algorithm is determined by the unique solution of a convex optimization problem independent from the distribution of random communication graphs.

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