There is no variational characterization of the cycles in the method of periodic projections
| Autor: | Jean-Bernard Baillon, Patrick L. Combettes, Roberto Cominetti |
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| Přispěvatelé: | Statistique, Analyse et Modélisation Multidisciplinaire (SAmos-Marin Mersenne) (SAMM), Université Paris 1 Panthéon-Sorbonne (UP1), Université Pierre et Marie Curie - Paris 6 (UPMC), Departamento de Ingenieria Industrial [Santiago] (DII), Laboratoire Jacques-Louis Lions (LJLL), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS) |
| Jazyk: | angličtina |
| Předmět: |
Pure mathematics
Alternating projections 47N10 Université Pierre et Marie Curie Von Neumann algorithm Corresponding author: P L Combettes 0211 other engineering and technologies Proper convex function Convex set Laboratoire Jacques-Louis Lions 02 engineering and technology Subderivative 01 natural sciences 75005 Paris Combinatorics symbols.namesake phone: +33 1 4427 6319 FOS: Mathematics plc@mathjussieufr fax: +33 1 4427 7200 0101 mathematics Dykstra's projection algorithm Mathematics Convex analysis 021103 operations research 010102 general mathematics Hilbert space 65K15 sadco Limit cycle von Neumann algo-rithm 2010 Mathematics Subject Classification 47H09 Functional Analysis (math.FA) Mathematics - Functional Analysis 4 place Jussieu Convex optimization symbols Best approximation France [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC] Convex function Analysis 47H10 |
| Zdroj: | Journal of Functional Analysis Journal of Functional Analysis, 2012, 262, pp.400-408. ⟨10.1016/j.jfa.2011.09.002⟩ Journal of Functional Analysis, 2012, 262 (1), pp.400-408. ⟨10.1016/j.jfa.2011.09.002⟩ Journal of Functional Analysis, Elsevier, 2012, 262 (1), pp.400-408. ⟨10.1016/j.jfa.2011.09.002⟩ Journal of Functional Analysis, Elsevier, 2012, 262, pp.400-408. ⟨10.1016/j.jfa.2011.09.002⟩ JOURNAL OF FUNCTIONAL ANALYSIS Artículos CONICYT CONICYT Chile instacron:CONICYT |
| ISSN: | 0022-1236 1096-0783 |
| DOI: | 10.1016/j.jfa.2011.09.002 |
| Popis: | International audience; 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. |
| Databáze: | OpenAIRE |
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