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arXiv · 1703.05233

A Distributed Algorithm for Computing a Common Fixed Point of a Finite Family of Paracontractions

Daniel Fullmer·A. Stephen Morse
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Abstract

A distributed algorithm is described for finding a common fixed point of a family of m>1 nonlinear maps M_i : R^n -> R^n assuming that each map is a paracontraction and that at least one such common fixed point exists. The common fixed point is simultaneously computed by m agents assuming each agent i knows only M_i, the current estimates of the fixed point generated by its neighbors, and nothing more. Each agent recursively updates its estimate of a fixed point by utilizing the current estimates generated by each of its neighbors. Neighbor relations are characterized by a time-varying directed graph N(t). It is shown under suitably general conditions on N(t), that the algorithm causes all agents estimates to converge to the same common fixed point of the m nonlinear maps.

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Daniel Fullmer, A. Stephen Morse. 2017-03-15. A Distributed Algorithm for Computing a Common Fixed Point of a Finite Family of Paracontractions. https://doi.org/10.1109/tac.2018.2800644

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