Algorithms Based on Unions of Nonexpansive Maps

Alexander J. Zaslavski
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Alexander J. Zaslavski: Technion, Israel Institute of Technology

Chapter Chapter 6 in Solutions of Fixed Point Problems with Computational Errors, 2024, pp 251-335 from Springer

Abstract: Abstract 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.

Date: 2024
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DOI: 10.1007/978-3-031-50879-0_6

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