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

Jean-Bernard Baillon 1 Patrick Louis Combettes 2 Roberto Cominetti 3
1 SAMM - Statistique, Analyse et Modélisation Multidisciplinaire (SAmos-Marin Mersenne)
2 LJLL - Laboratoire Jacques-Louis Lions
3 DII - Departamento de Ingenieria Industrial [Santiago]
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.
keyword : sadco
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Journal of Functional Analysis, Elsevier, 2012, 262 (1), pp.400-408. 〈10.1016/j.jfa.2011.09.002〉
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https://hal.inria.fr/hal-00643370
Contributeur : Estelle Bouzat <>
Soumis le : lundi 21 novembre 2011 - 16:58:24
Dernière modification le : vendredi 31 août 2018 - 09:06:02

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Jean-Bernard Baillon, Patrick Louis Combettes, Roberto Cominetti. There is no variational characterization of the cycles in the method of periodic projections. Journal of Functional Analysis, Elsevier, 2012, 262 (1), pp.400-408. 〈10.1016/j.jfa.2011.09.002〉. 〈hal-00643370〉

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