The expected-projection method: Its behavior and applications to linear operator equations and convex optimization

Research output: Contribution to journalArticlepeer-review

Abstract

It was shown by Butnariu and Flåm [5] that under some conditions, sequences generated by the expected projection method (EPM) in Hilbert spaces approximate almost common points of measurable families of closed convex subsets provided that such points exist. In this work we study the behavior of the EPM in the more general situation when the involved sets may or may not have almost common points and we give necessary and sufficient conditions for weak and strong convergence. Also, we show how the EPM can be applied to finding solutions of linear operator equations and to solving convex optimization problems.

Original languageEnglish
Pages (from-to)93-108
Number of pages16
JournalJournal of Applied Analysis
Volume1
Issue number1
DOIs
StatePublished - 1995

Keywords

  • asymptotic center of sequence
  • Bochner integral
  • Convex set
  • metric projection
  • optimization problem
  • stochastic convex feasibility problem

ASJC Scopus subject areas

  • Mathematical Physics
  • Statistics, Probability and Uncertainty
  • Computational Theory and Mathematics
  • Applied Mathematics

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