Full Text: PDF
DOI: 10.23952/cot.2024.9
Received July 10, 2023; Accepted August 8, 2023; Published online October 27, 2023
Abstract. Recently, M.K. Tam considered a framework for the analysis of iterative algorithms which can be described in terms of a structured set-valued operator in 2018. At each point in the ambient space, the value of the operator is expressed as a finite union of values of single-valued paracontracting operators. Tam proved that the associated fixed point iteration is locally convergent around strong fixed points. We generalize Tam’s result and investigate the global convergence of his algorithm for an arbitrary starting point. In this paper, this result is generalized for an operator expressed as a finite union of values of single-valued quasi-nonexpansive operators.
How to Cite this Article:
A.J. Zaslavski, Convergence of algorithms based on unions of quasi-nonexpansive maps, Commun. Optim. Theory 2024 (2024) 9.