A contraction proximal point algorithm with two monotone operators

Oganeditse A. Boikanyo, Gheorghe Moroşanu

Research output: Contribution to journalArticle

5 Citations (Scopus)

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. If 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.

Original languageEnglish
Pages (from-to)5686-5692
Number of pages7
JournalNonlinear Analysis, Theory, Methods and Applications
Volume75
Issue number14
DOIs
Publication statusPublished - Sep 1 2012

Fingerprint

Proximal Point Algorithm
Monotone Operator
Alternating Projections
Mathematical operators
Contraction
Indicator function
Maximal Monotone Operator
Subdifferential
Iterative Process
Strong Convergence
Convergence Results
Hilbert spaces
Hilbert space
Set theory
Converge
Closed
Generalise
Subset
Zero
Arbitrary

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

Cite this

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A contraction proximal point algorithm with two monotone operators. / Boikanyo, Oganeditse A.; Moroşanu, Gheorghe.

In: Nonlinear Analysis, Theory, Methods and Applications, Vol. 75, No. 14, 01.09.2012, p. 5686-5692.

Research output: Contribution to journalArticle

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