Inexact Halpern-type proximal point algorithm

O. A. Boikanyo, G. Moroşanu

Research output: Contribution to journalArticle

22 Citations (Scopus)

Abstract

We present several strong convergence results for the modified, Halpern-type, proximal point algorithm xn+1 = αnu + (1 - αn)Jβn xn + en (n = 0, 1, . . .; u, x0 ∈ H given, and Jβn = (I+βnA)-1, for a maximal monotone operator A) in a real Hilbert space, under new sets of conditions on αn ∈ (0,1) and βn ∈ (0,∞). These conditions are weaker than those known to us and our results extend and improve some recent results such as those of H. K. Xu. We also show how to apply our results to approximate minimizers of convex functionals. In addition, we give convergence rate estimates for a sequence approximating the minimum value of such a functional.

Original languageEnglish
Pages (from-to)11-26
Number of pages16
JournalJournal of Global Optimization
Volume51
Issue number1
DOIs
Publication statusPublished - Sep 1 2011

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Proximal Point Algorithm
Hilbert spaces
Mathematical operators
Maximal Monotone Operator
Strong Convergence
Minimizer
Convergence Results
Convergence Rate
Hilbert space
Estimate
Convergence rate
Operator

All Science Journal Classification (ASJC) codes

  • Computer Science Applications
  • Control and Optimization
  • Management Science and Operations Research
  • Applied Mathematics

Cite this

Boikanyo, O. A. ; Moroşanu, G. / Inexact Halpern-type proximal point algorithm. In: Journal of Global Optimization. 2011 ; Vol. 51, No. 1. pp. 11-26.
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Inexact Halpern-type proximal point algorithm. / Boikanyo, O. A.; Moroşanu, G.

In: Journal of Global Optimization, Vol. 51, No. 1, 01.09.2011, p. 11-26.

Research output: Contribution to journalArticle

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