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Article Dans Une Revue Foundations of Computational Mathematics Année : 2009

Local linear convergence of alternating and averaged nonconvex projections

Résumé

The idea of a finite collection of closed sets having "linearly regular intersection" at a point is crucial in variational analysis. This central theoretical condition also has striking algorithmic consequences: in the case of two sets, one of which satisfies a further regularity condition (convexity or smoothness, for example), we prove that von Neumann's method of "alternating projections" converges locally to a point in the intersection, at a linear rate associated with a modulus of regularity. As a consequence, in the case of several arbitrary closed sets having linearly regular intersection at some point, the method of "averaged projections" converges locally at a linear rate to a point in the intersection. Inexact versions of both algorithms also converge linearly.
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Dates et versions

hal-00389555 , version 1 (02-06-2009)

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Adrian Lewis, David Russel Luke, Jérôme Malick. Local linear convergence of alternating and averaged nonconvex projections. Foundations of Computational Mathematics, 2009, 9 (4), pp.485-513. ⟨10.1007/s10208-008-9036-y⟩. ⟨hal-00389555⟩
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