Relatively inexact proximal point algorithm and linear convergence analysis
type: Item
instance of: scholarly article
title: Relatively inexact proximal point algorithm and linear convergence analysis
zbMATH Open document ID: 1185.49034
DOI: 10.1155/2009/691952
author: Ram U. Verma
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2010-04-20T00:00:00Z
full work available at URL: https://eudml.org/doc/226599
review text: Summary: Based on a notion of relatively maximal \((m)\)-relaxed monotonicity, the approximation solvability of a general class of inclusion problems is discussed, while generalizing \textit{R. T. Rockafellar}'s theorem [Math. Oper. Res. 1, 97--116 (1976; Zbl 0402.90076)] on linear convergence using the proximal point algorithm in a real Hilbert space setting. Convergence analysis, based on this new model, is simpler and more compact than that of the celebrated technique of Rockafellar in which the Lipschitz continuity at 0 of the inverse of the set-valued mapping is applied. Furthermore, it can be used to generalize the Yosida approximation, which, in turn, can be applied to first-order evolution equations as well as evolution inclusions.
Mathematics Subject Classification ID: 49M30
Mathematics Subject Classification ID: 90C25
zbMATH DE Number: 5695224
zbMATH Keywords: relatively maximal \((m)\)-relaxed monotonicity
zbMATH Keywords: Rockafellar's theorem
zbMATH Keywords: convergence analysis
zbMATH Keywords: Yosida approximation
Wikidata QID: Q58648500
MaRDI profile type: Publication
OpenAlex ID: W2009467175
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description: scientific article; zbMATH DE number 5695224