A proximal point algorithm converging strongly for general errors

O. A. Boikanyo, G. Moroşanu

Research output: Contribution to journalArticle

47 Citations (Scopus)

Abstract

In this paper a proximal point algorithm (PPA) for maximal monotone operators with appropriate regularization parameters is considered. A strong convergence result for PPA is stated and proved under the general condition that the error sequence tends to zero in norm. Note that Rockafellar (SIAM J Control Optim 14:877-898, 1976) assumed summability for the error sequence to derive weak convergence of PPA in its initial form, and this restrictive condition on errors has been extensively used so far for different versions of PPA. Thus this Note provides a solution to a long standing open problem and in particular offers new possibilities towards the approximation of the minimum points of convex functionals.

Original languageEnglish
Pages (from-to)635-641
Number of pages7
JournalOptimization Letters
Volume4
Issue number4
DOIs
Publication statusPublished - Feb 5 2010

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Proximal Point Algorithm
Maximal Monotone Operator
Regularization Parameter
Summability
Weak Convergence
Strong Convergence
Convergence Results
Open Problems
Tend
Norm
Zero
Approximation

All Science Journal Classification (ASJC) codes

  • Control and Optimization

Cite this

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A proximal point algorithm converging strongly for general errors. / Boikanyo, O. A.; Moroşanu, G.

In: Optimization Letters, Vol. 4, No. 4, 05.02.2010, p. 635-641.

Research output: Contribution to journalArticle

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