Four parameter proximal point algorithms
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Subtitle: Four parameter proximal point algorithms
Publisher: Institute of Mathematics and Informatics
Publication year: 2011
Volume number: 74
Issue number: 2
Start page: 544
End page: 555
Number of pages: 12
ISSN: 1392-5113
URL: https://www.sciencedirect.com
Languages: English-United States (EN-US)
Abstract
Several strong convergence results involving two distinct four parameter proximal point algorithms are proved under different sets of assumptions on these parameters and the general condition that the error sequence converges to zero in norm. Thus our results address the two important problems related to the proximal point algorithm one being that of strong convergence (instead of weak convergence) and the other one being that of acceptable errors. One of the algorithms discussed was introduced by Yao and Noor (2008) [7] while the other one is new and it is a generalization of the regularization method initiated by Lehdili and Moudafi (1996) [9] and later developed by Xu (2006) [8]. The new algorithm is also ideal for estimating the convergence rate of a sequence that approximates minimum values of certain functionals. Although these algorithms are distinct, it turns out that for a particular case, they are equivalent. The results of this paper extend and generalize several existing ones in the literature.
Keywords
Proximal point algorithmRegularization methodMonotone operatorWeak convergenceStrong convergenceMinimizer
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