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Article Dans Une Revue Journal of Functional Analysis Année : 2012

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

Résumé

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 that minimize smooth convex functions over a product of convex sets are also discussed.
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Dates et versions

hal-01077039 , version 1 (23-10-2014)

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Jean-Bernard Baillon, Patrick Louis Combettes, R Cominetti. There is no variational characterization of the cycles in the method of periodic projections. Journal of Functional Analysis, 2012, 262, pp.400 - 408. ⟨10.1016/j.jfa.2011.09.002⟩. ⟨hal-01077039⟩
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