Distributed computation of fixed points of \(\infty\)-nonexpansive maps (Q1126318)

The paper deals with a distributed implementation of an algorithm for finding a fixed point of a \(\text{map }F: \mathbb{R}^d\to \mathbb{R}^d\) which is nonexpansive with respect to the \(\infty\)-norm. It is proved that the proposed algorithm converges to the set of fixed points under general conditions. Finally, it is shown that numerical analysis and optimization problems such as shortest path problems, Markov decision processes, systems of linear equations, strictly convex network flow problems can be cast as problems of finding fixed points of \(\infty\)-nonexpansive maps.