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

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2012-01-01
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Baillon, Jean-Bernard
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There is no variational characterization of the cycles in the method of periodic projections
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Author
  • Baillon, Jean-Bernard;
  • Combettes, P. L.;
  • Cominetti Cotti-Cometti, Roberto;
Abstract
The method of periodic projections consists in iterating projections onto in closed convex subsets of a Hilbert space according to a periodic sweeping strategy. In the presence of in 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.
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Agence Nationale de la Recherche ANR-08-BLAN-0294-02 FONDECYT 1100046 Instituto Milenio Sistemas Complejos en Ingenieria
Identifier
URI: https://repositorio.uchile.cl/handle/2250/125600
DOI: DOI: 10.1016/j.jfa.2011.09.002
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JOURNAL OF FUNCTIONAL ANALYSIS Volume: 262 Issue: 1 Pages: 400-408 Published: JAN 1 2012
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