A contraction proximal point algorithm with two monotone operators

TitleA contraction proximal point algorithm with two monotone operators
Publication TypeJournal Article
AuthorsBoikanyo, Oganeditse A., and Gheorghe Morosanu
Journal title Nonlinear Analysis
Year2012
Pages5686–5692
Volume75
Abstract

It is a known fact that the method of alternating projections introduced long ago by
von Neumann fails to converge strongly for two arbitrary nonempty, closed and convex subsets
of a real Hilbert space. In this paper, a new iterative process for finding common zeros of two
maximal monotone operators is introduced and strong convergence results associated with it are
proved. For the case when the two operators are subdifferentials of indicator functions, this new
algorithm coincides with the old method of alternating projections. Several other important algorithms,
such as the contraction proximal point algorithm, occur as special cases of our algorithm.
Hence our main results generalize and unify many results that occur in the literature.

LanguageEnglish
Notes

to appear

DOIdoi:10.1016/j.na.2012.05.016
Publisher linkhttp://www.sciencedirect.com/science/article/pii/S0362546X12002143
Unit: 
Department of Mathematics and its Applications
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