Four parameter proximal point algorithms

TitleFour parameter proximal point algorithms
Publication TypeJournal Article
AuthorsBoikanyo, Oganeditse A., and Gheorghe Morosanu
Journal titleNonlinear Analysis

Several strong convergence results involving two distinct fourparameterproximalpointalgorithms 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 proximalpointalgorithm — 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.

Publisher link
Department of Mathematics and its Applications
File attachment: