Algorithms Based on Unions of Nonexpansive Maps

In this chapter we analyze iterative algorithms, which can be described in terms of a structured set-valued operator. Namely, at every point in the ambient space, it is assumed that the value of the operator can be expressed as a finite union of values of single-valued quasi-nonexpansive operators. For such algorithms it is shown their global convergence for an arbitrary starting point. An analogous result is also proved for the Krasnosel’ski-Mann iterations.