Convergence rate and termination of asynchronous iterative algorithms

Authors:
Dimitri P. Bertsekas;John N. Tsitsiklis
Affiliations:
Laboratory for Information and Decision Systems, Massachusetts Institute of Technology, Cambridge, MA;Laboratory for Information and Decision Systems, Massachusetts Institute of Technology, Cambridge, MA
Venue:
ICS '89 Proceedings of the 3rd international conference on Supercomputing
Year:
1989

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Abstract

We consider iterative algorithms of the form x := ƒ(x), executed by a parallel or distributed computing system. We focus on asynchronous implementations whereby each processor iterates on a different component of x, at its own pace, using the most recently received (but possibly outdated) information on the remaining components of x. We provide results on the convergence rate of such algorithms and make a comparison with the convergence rate of the corresponding synchronous methods in which the computation proceeds in phases. We also present results on how to terminate asynchronous iterations in finite time with an approximate solution of the computational problem under consideration.