Asymptotic behaviour of a family of gradient algorithms in R^d and Hilbert spaces

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dc.creatorPronzato, Luc
dc.creatorWynn, Henry P.
dc.creatorZhigljavsky, Anatoly A.
dc.date2008-02-29
dc.date.accessioned2026-07-07T09:24:04Z
dc.date.available2026-07-07T09:24:04Z
dc.descriptionThe asymptotic behaviour of a family of gradient algorithms (including the methods of steepest descent and minimum residues) for the optimisation of bounded quadratic operators in R^d and Hilbert spaces is analyzed. The results obtained generalize those of Akaike (1959) in several directions. First, all algorithms in the family are shown to have the same asymptotic behaviour (convergence to a two-point attractor), which implies in particular that they have similar asymptotic convergence rates. Second, the analysis also covers the Hilbert space case. A detailed analysis of the stability property of the attractor is provided.
dc.descriptionThe original publication is available at http://www.springerlink.com
dc.identifierhttps://arxiv.org/abs/0802.4382
dc.identifierhttp://arxiv.org/abs/0802.4382
dc.identifierMathematical Programming, Series A 107 (2006) 409-438
dc.identifierdoi:10.1007/s10107-005-0602-7
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/155963
dc.subjectOptimization and Control
dc.subject90C25, 68Q25
dc.titleAsymptotic behaviour of a family of gradient algorithms in R^d and Hilbert spaces
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