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.
Mots clés
65K15
Corresponding author: P L Combettes
alternating projections
best approximation
limit cycle
von Neumann algo-rithm 2010 Mathematics Subject Classification 47H09
47H10
47N10
plc@mathjussieufr
Laboratoire Jacques-Louis Lions
Université Pierre et Marie Curie
4 place Jussieu
75005 Paris
France
phone: +33 1 4427 6319
fax: +33 1 4427 7200
Domaines
Optimisation et contrôle [math.OC]
Origine : Fichiers produits par l'(les) auteur(s)
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