Inexact Halpern-type proximal point algorithm

O. A. Boikanyo, G. Moroşanu

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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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All Science Journal Classification (ASJC) codes

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

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