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

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.
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https://hal.inria.fr/hal-00643370
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Submitted on : Monday, November 21, 2011 - 4:58:24 PM
Last modification on : Friday, May 6, 2022 - 4:50:07 PM

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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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