Abstract
An approximate diagonal version of the iteration method for a nonexpansive self mapping of a Banach space (hence with possible non unique fixed-point if any) is considered. Two kinds of properties satisfied by this method that cover widely recent results on the prox or gradient-prox method for convex optimization and monotone inclusions are presented: localization and selection.
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Lemaire, B. (1997). Which Fixed Point Does the Iteration Method Select?. In: Gritzmann, P., Horst, R., Sachs, E., Tichatschke, R. (eds) Recent Advances in Optimization. Lecture Notes in Economics and Mathematical Systems, vol 452. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-59073-3_11
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DOI: https://doi.org/10.1007/978-3-642-59073-3_11
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