On the method of alternating resolvents

Oganeditse A. Boikanyo, Gheorghe Moroanu

Research output: Contribution to journalArticle

11 Citations (Scopus)

Abstract

The work of Hundal [H. Hundal, An alternating projection that does not converge in norm, Nonlinear Anal. 57 (1) (2004) 3561] has revealed that the sequence generated by the method of alternating projections converges weakly, but not strongly in general. In this paper, we present several algorithms based on alternating resolvents of two maximal monotone operators, A and B, that can be used to approximate common zeros of A and B. In particular, we prove that the sequences generated by our algorithms converge strongly. A particular case of such algorithms enables one to approximate minimum values of certain convex functionals.

Original languageEnglish
Pages (from-to)5147-5160
Number of pages14
JournalNonlinear Analysis, Theory, Methods and Applications
Volume74
Issue number15
DOIs
Publication statusPublished - Oct 1 2011

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All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

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