Pré-Publication, Document De Travail Année : 2013

Splitting methods with variable metric for KL functions

Résumé

We study the convergence of general abstract descent methods applied to a lower semicontinuous nonconvex function f that satisfies the Kurdyka-Lojasiewicz inequality in a Hilbert space. We prove that any precompact sequence converges to a critical point of f and obtain new convergence rates both for the values and the iterates. The analysis covers alternating versions of the forward-backward method with variable metric and relative errors. As an example, a nonsmooth and nonconvex version of the Levenberg-Marquardt algorithm is detailled.

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Dates et versions

hal-00987523 , version 1 (06-05-2014)
hal-00987523 , version 2 (07-07-2014)

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Pierre Frankel, Guillaume Garrigos, Juan Peypouquet. Splitting methods with variable metric for KL functions. 2013. ⟨hal-00987523v2⟩
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