There is no variational characterization of the cycles in the method of periodic projections

J. B. Baillon, P. L. Combettes, R. Cominetti

Research output: Contribution to journalArticlepeer-review

17 Scopus citations

Abstract

The method of periodic projections consists in iterating projections onto. m closed convex subsets of a Hilbert space according to a periodic sweeping strategy. In the presence of. m≥. 3 sets, a long-standing question going back to the 1960s is whether the limit cycles obtained by such a process can be characterized as the minimizers of a certain functional. In this paper we answer this question in the negative. Projection algorithms for minimizing smooth convex functions over a product of convex sets are also discussed.

Original languageEnglish
Pages (from-to)400-408
Number of pages9
JournalJournal of Functional Analysis
Volume262
Issue number1
DOIs
StatePublished - 1 Jan 2012

Keywords

  • Alternating projections
  • Best approximation
  • Limit cycle
  • Von Neumann algorithm

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